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Номер 896, страница 249 - гдз по алгебре 9 класс учебник Солтан, Солтан
Авторы: Солтан Г. Н., Солтан А. Е., Жумадилова А. Ж.
Тип: Учебник
Издательство: Кокшетау
Год издания: 2019 - 2026
ISBN: 978-601-317-424-2
Рекомендовано Министерством образования и науки Республики Казахстан
Популярные ГДЗ в 9 классе
Повторение курса алгебры 7-9 классов. Числовые и алгебраические выражения и их преобразования - номер 896, страница 249.
App\Models\Task {#1030 // resources/views/models/task/default.blade.php #connection: "mysql" #table: "tasks" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ "id" => 1108651 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "249" "field_page_end" => null "field_url" => "/9-klass/algebra/kokshetau-soltan-uchebnik/1-896" "field_display_title" => "896" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1037 #items: array:1 [ 0 => App\Models\Term {#1036 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 26 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "номер" "field_cases" => array:6 [ "field_accusative_case" => "номер" "field_creative_case" => "номером" "field_dative_case" => "номеру" "field_genitive_case" => "номера" "field_nominative_case" => "номер" "field_prepositional_case" => "номере" ] "field_short_name" => "№" ] #original: array:6 [ "id" => 26 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "номер" "field_cases" => array:6 [ "field_accusative_case" => "номер" "field_creative_case" => "номером" "field_dative_case" => "номеру" "field_genitive_case" => "номера" "field_nominative_case" => "номер" "field_prepositional_case" => "номере" ] "field_short_name" => "№" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#1035 #items: [] #escapeWhenCastingToString: false } "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1071 #items: array:1 [ 0 => App\Models\Branch {#1034 #connection: "mysql" #table: "branches" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ "id" => 1107678 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Повторение курса алгебры 7-9 классов" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1039 #items: [] #escapeWhenCastingToString: false } "field_page_start" => "249" "field_branch_display" => "0" "field_branch_expanded" => "0" "field_display_branch_in_title" => "1" "field_display_task_interval" => "0" "field_display_branch_page" => "1" "field_branch_title_in_content" => "0" "field_navigation_title" => null "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_branch_cover" => [] "field_branch_covers" => [] "book" => Illuminate\Database\Eloquent\Collection {#1038 #items: array:1 [ 0 => App\Models\Book {#1040 #connection: "mysql" #table: "books" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:50 [ "id" => 4298 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_tree_default_status" => "tasks" "field_pages_status" => null "field_subject" => Illuminate\Database\Eloquent\Collection {#1041 …2} "field_class" => Illuminate\Database\Eloquent\Collection {#1043 …2} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1045 …2} "field_author" => Illuminate\Database\Eloquent\Collection {#1047 …2} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1051 …2} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1052 …2} "field_country" => Illuminate\Database\Eloquent\Collection {#1054 …2} "field_city" => Illuminate\Database\Eloquent\Collection {#1056 …2} "field_series" => Illuminate\Database\Eloquent\Collection {#1058 …2} "field_umk" => Illuminate\Database\Eloquent\Collection {#1059 …2} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1060 …2} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1061 …2} "field_publication_number" => null "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1062 …2} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1063 …2} "field_under_the_edition_degree" => null "field_cover_description" => null "field_publication_year" => "2019" "field_publication_year_until" => null "field_part" => "" "field_part_writing" => "" "field_second_foreign_language" => null "field_for_whom" => "Учебник для учащихся 9 класса общеобразовательных школ" "field_allowed" => "Рекомендовано Министерством образования и науки Республики Казахстан" "field_reserve_field" => null "field_link_to_source" => null "field_tasks_count" => "1291" "field_priority" => "4" "field_default_folder" => "/algebra_09/soltan-u19/" "field_isbn" => "978-601-317-424-2" "field_cover" => array:1 [ …1] "field_cover_alts" => array:1 [ …1] "field_covers" => array:1 [ …1] "field_popular_book" => null "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1064 …2} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1065 …2} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1066 …2} "field_url" => "/9-klass/algebra/kokshetau-soltan-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1067 …2} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "breadcrumbs" => array:3 [ …3] ] #original: array:50 [ "id" => 4298 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_tree_default_status" => "tasks" "field_pages_status" => null "field_subject" => Illuminate\Database\Eloquent\Collection {#1041 …2} "field_class" => Illuminate\Database\Eloquent\Collection {#1043 …2} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1045 …2} "field_author" => Illuminate\Database\Eloquent\Collection {#1047 …2} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1051 …2} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1052 …2} "field_country" => Illuminate\Database\Eloquent\Collection {#1054 …2} "field_city" => Illuminate\Database\Eloquent\Collection {#1056 …2} "field_series" => Illuminate\Database\Eloquent\Collection {#1058 …2} "field_umk" => Illuminate\Database\Eloquent\Collection {#1059 …2} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1060 …2} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1061 …2} "field_publication_number" => null "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1062 …2} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1063 …2} "field_under_the_edition_degree" => null "field_cover_description" => null "field_publication_year" => "2019" "field_publication_year_until" => null "field_part" => "" "field_part_writing" => "" "field_second_foreign_language" => null "field_for_whom" => "Учебник для учащихся 9 класса общеобразовательных школ" "field_allowed" => "Рекомендовано Министерством образования и науки Республики Казахстан" "field_reserve_field" => null "field_link_to_source" => null "field_tasks_count" => "1291" "field_priority" => "4" "field_default_folder" => "/algebra_09/soltan-u19/" "field_isbn" => "978-601-317-424-2" "field_cover" => array:1 [ …1] "field_cover_alts" => array:1 [ …1] "field_covers" => array:1 [ …1] "field_popular_book" => null "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1064 …2} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1065 …2} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1066 …2} "field_url" => "/9-klass/algebra/kokshetau-soltan-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1067 …2} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "breadcrumbs" => array:3 [ …3] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1068 #items: [] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 1107678 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Повторение курса алгебры 7-9 классов" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1039} "field_page_start" => "249" "field_branch_display" => "0" "field_branch_expanded" => "0" "field_display_branch_in_title" => "1" "field_display_task_interval" => "0" "field_display_branch_page" => "1" "field_branch_title_in_content" => "0" "field_navigation_title" => null "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_branch_cover" => [] "field_branch_covers" => [] "book" => Illuminate\Database\Eloquent\Collection {#1038} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1068} ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "parent_branches" => Illuminate\Database\Eloquent\Collection {#1138 #items: array:2 [ 0 => App\Models\Branch {#1069 #connection: "mysql" #table: "branches" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ "id" => 1107678 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Повторение курса алгебры 7-9 классов" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1072 #items: [] #escapeWhenCastingToString: false } "field_page_start" => "249" "field_branch_display" => "0" "field_branch_expanded" => "0" "field_display_branch_in_title" => "1" "field_display_task_interval" => "0" "field_display_branch_page" => "1" "field_branch_title_in_content" => "0" "field_navigation_title" => null "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_branch_cover" => [] "field_branch_covers" => [] "book" => Illuminate\Database\Eloquent\Collection {#1070 #items: array:1 [ 0 => App\Models\Book {#1073 #connection: "mysql" #table: "books" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:50 [ "id" => 4298 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_tree_default_status" => "tasks" "field_pages_status" => null "field_subject" => Illuminate\Database\Eloquent\Collection {#1074 …2} "field_class" => Illuminate\Database\Eloquent\Collection {#1076 …2} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1078 …2} "field_author" => Illuminate\Database\Eloquent\Collection {#1080 …2} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1084 …2} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1085 …2} "field_country" => Illuminate\Database\Eloquent\Collection {#1087 …2} "field_city" => Illuminate\Database\Eloquent\Collection {#1089 …2} "field_series" => Illuminate\Database\Eloquent\Collection {#1091 …2} "field_umk" => Illuminate\Database\Eloquent\Collection {#1092 …2} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1093 …2} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1094 …2} "field_publication_number" => null "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1095 …2} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1096 …2} "field_under_the_edition_degree" => null "field_cover_description" => null "field_publication_year" => "2019" "field_publication_year_until" => null "field_part" => "" "field_part_writing" => "" "field_second_foreign_language" => null "field_for_whom" => "Учебник для учащихся 9 класса общеобразовательных школ" "field_allowed" => "Рекомендовано Министерством образования и науки Республики Казахстан" "field_reserve_field" => null "field_link_to_source" => null "field_tasks_count" => "1291" "field_priority" => "4" "field_default_folder" => "/algebra_09/soltan-u19/" "field_isbn" => "978-601-317-424-2" "field_cover" => array:1 [ …1] "field_cover_alts" => array:1 [ …1] "field_covers" => array:1 [ …1] "field_popular_book" => null "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1097 …2} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1098 …2} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1099 …2} "field_url" => "/9-klass/algebra/kokshetau-soltan-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1100 …2} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "breadcrumbs" => array:3 [ …3] ] #original: array:50 [ "id" => 4298 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_tree_default_status" => "tasks" "field_pages_status" => null "field_subject" => Illuminate\Database\Eloquent\Collection {#1074 …2} "field_class" => Illuminate\Database\Eloquent\Collection {#1076 …2} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1078 …2} "field_author" => Illuminate\Database\Eloquent\Collection {#1080 …2} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1084 …2} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1085 …2} "field_country" => Illuminate\Database\Eloquent\Collection {#1087 …2} "field_city" => Illuminate\Database\Eloquent\Collection {#1089 …2} "field_series" => Illuminate\Database\Eloquent\Collection {#1091 …2} "field_umk" => Illuminate\Database\Eloquent\Collection {#1092 …2} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1093 …2} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1094 …2} "field_publication_number" => null "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1095 …2} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1096 …2} "field_under_the_edition_degree" => null "field_cover_description" => null "field_publication_year" => "2019" "field_publication_year_until" => null "field_part" => "" "field_part_writing" => "" "field_second_foreign_language" => null "field_for_whom" => "Учебник для учащихся 9 класса общеобразовательных школ" "field_allowed" => "Рекомендовано Министерством образования и науки Республики Казахстан" "field_reserve_field" => null "field_link_to_source" => null "field_tasks_count" => "1291" "field_priority" => "4" "field_default_folder" => "/algebra_09/soltan-u19/" "field_isbn" => "978-601-317-424-2" "field_cover" => array:1 [ …1] "field_cover_alts" => array:1 [ …1] "field_covers" => array:1 [ …1] "field_popular_book" => null "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1097 …2} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1098 …2} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1099 …2} "field_url" => "/9-klass/algebra/kokshetau-soltan-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1100 …2} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "breadcrumbs" => array:3 [ …3] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1101 #items: [] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 1107678 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Повторение курса алгебры 7-9 классов" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1072} "field_page_start" => "249" "field_branch_display" => "0" "field_branch_expanded" => "0" "field_display_branch_in_title" => "1" "field_display_task_interval" => "0" "field_display_branch_page" => "1" "field_branch_title_in_content" => "0" "field_navigation_title" => null "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_branch_cover" => [] "field_branch_covers" => [] "book" => Illuminate\Database\Eloquent\Collection {#1070} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1101} ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 1 => App\Models\Branch {#1102 #connection: "mysql" #table: "branches" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ "id" => 1107679 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Числовые и алгебраические выражения и их преобразования" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1103 #items: [] #escapeWhenCastingToString: false } "field_page_start" => "249" "field_branch_display" => "0" "field_branch_expanded" => "0" "field_display_branch_in_title" => "1" "field_display_task_interval" => "0" "field_display_branch_page" => "1" "field_branch_title_in_content" => "0" "field_navigation_title" => null "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_branch_cover" => [] "field_branch_covers" => [] "book" => Illuminate\Database\Eloquent\Collection {#1104 #items: array:1 [ 0 => App\Models\Book {#1105 #connection: "mysql" #table: "books" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:50 [ "id" => 4298 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_tree_default_status" => "tasks" "field_pages_status" => null "field_subject" => Illuminate\Database\Eloquent\Collection {#1106 …2} "field_class" => Illuminate\Database\Eloquent\Collection {#1108 …2} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1110 …2} "field_author" => Illuminate\Database\Eloquent\Collection {#1112 …2} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1116 …2} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1117 …2} "field_country" => Illuminate\Database\Eloquent\Collection {#1119 …2} "field_city" => Illuminate\Database\Eloquent\Collection {#1121 …2} "field_series" => Illuminate\Database\Eloquent\Collection {#1123 …2} "field_umk" => Illuminate\Database\Eloquent\Collection {#1124 …2} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1125 …2} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1126 …2} "field_publication_number" => null "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1127 …2} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1128 …2} "field_under_the_edition_degree" => null "field_cover_description" => null "field_publication_year" => "2019" "field_publication_year_until" => null "field_part" => "" "field_part_writing" => "" "field_second_foreign_language" => null "field_for_whom" => "Учебник для учащихся 9 класса общеобразовательных школ" "field_allowed" => "Рекомендовано Министерством образования и науки Республики Казахстан" "field_reserve_field" => null "field_link_to_source" => null "field_tasks_count" => "1291" "field_priority" => "4" "field_default_folder" => "/algebra_09/soltan-u19/" "field_isbn" => "978-601-317-424-2" "field_cover" => array:1 [ …1] "field_cover_alts" => array:1 [ …1] "field_covers" => array:1 [ …1] "field_popular_book" => null "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1129 …2} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1130 …2} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1131 …2} "field_url" => "/9-klass/algebra/kokshetau-soltan-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1132 …2} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "breadcrumbs" => array:3 [ …3] ] #original: array:50 [ "id" => 4298 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_tree_default_status" => "tasks" "field_pages_status" => null "field_subject" => Illuminate\Database\Eloquent\Collection {#1106 …2} "field_class" => Illuminate\Database\Eloquent\Collection {#1108 …2} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1110 …2} "field_author" => Illuminate\Database\Eloquent\Collection {#1112 …2} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1116 …2} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1117 …2} "field_country" => Illuminate\Database\Eloquent\Collection {#1119 …2} "field_city" => Illuminate\Database\Eloquent\Collection {#1121 …2} "field_series" => Illuminate\Database\Eloquent\Collection {#1123 …2} "field_umk" => Illuminate\Database\Eloquent\Collection {#1124 …2} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1125 …2} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1126 …2} "field_publication_number" => null "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1127 …2} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1128 …2} "field_under_the_edition_degree" => null "field_cover_description" => null "field_publication_year" => "2019" "field_publication_year_until" => null "field_part" => "" "field_part_writing" => "" "field_second_foreign_language" => null "field_for_whom" => "Учебник для учащихся 9 класса общеобразовательных школ" "field_allowed" => "Рекомендовано Министерством образования и науки Республики Казахстан" "field_reserve_field" => null "field_link_to_source" => null "field_tasks_count" => "1291" "field_priority" => "4" "field_default_folder" => "/algebra_09/soltan-u19/" "field_isbn" => "978-601-317-424-2" "field_cover" => array:1 [ …1] "field_cover_alts" => array:1 [ …1] "field_covers" => array:1 [ …1] "field_popular_book" => null "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1129 …2} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1130 …2} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1131 …2} "field_url" => "/9-klass/algebra/kokshetau-soltan-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1132 …2} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "breadcrumbs" => array:3 [ …3] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1133 #items: array:1 [ 0 => App\Models\Branch {#1134 #connection: "mysql" #table: "branches" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ "id" => 1107678 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Повторение курса алгебры 7-9 классов" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1135 …2} "field_page_start" => "249" "field_branch_display" => "0" "field_branch_expanded" => "0" "field_display_branch_in_title" => "1" "field_display_task_interval" => "0" "field_display_branch_page" => "1" "field_branch_title_in_content" => "0" "field_navigation_title" => null "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_branch_cover" => [] "field_branch_covers" => [] "book" => Illuminate\Database\Eloquent\Collection {#1136 …2} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1137 …2} ] #original: array:24 [ "id" => 1107678 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Повторение курса алгебры 7-9 классов" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1135 …2} "field_page_start" => "249" "field_branch_display" => "0" "field_branch_expanded" => "0" "field_display_branch_in_title" => "1" "field_display_task_interval" => "0" "field_display_branch_page" => "1" "field_branch_title_in_content" => "0" "field_navigation_title" => null "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_branch_cover" => [] "field_branch_covers" => [] "book" => Illuminate\Database\Eloquent\Collection {#1136 …2} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1137 …2} ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 1107679 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Числовые и алгебраические выражения и их преобразования" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1103} "field_page_start" => "249" "field_branch_display" => "0" "field_branch_expanded" => "0" "field_display_branch_in_title" => "1" "field_display_task_interval" => "0" "field_display_branch_page" => "1" "field_branch_title_in_content" => "0" "field_navigation_title" => null "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_branch_cover" => [] "field_branch_covers" => [] "book" => Illuminate\Database\Eloquent\Collection {#1104} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1133} ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1156 #items: array:3 [ 0 => App\Models\Element {#1166 #connection: "mysql" #table: "elements" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:7 [ "id" => 1277251 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1175 #items: array:1 [ 0 => App\Models\Edition {#1167 #connection: "mysql" #table: "editions" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:21 [ "id" => 4953 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Условие" "field_order" => "1" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1169 …2} "field_content_type" => "free" "field_content_mode" => "text, image" "field_page_content_mode" => "image" "field_content_text_checked" => null "field_page_content_text_checked" => "0" "field_solution_author" => "Автор" "field_moderator" => "pasha" "field_edition_type" => "statement" "field_root_dir" => "0-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1170 …2} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1171 …2} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1172 …2} "field_content_source" => null ] #original: array:21 [ "id" => 4953 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Условие" "field_order" => "1" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1169 …2} "field_content_type" => "free" "field_content_mode" => "text, image" "field_page_content_mode" => "image" "field_content_text_checked" => null "field_page_content_text_checked" => "0" "field_solution_author" => "Автор" "field_moderator" => "pasha" "field_edition_type" => "statement" "field_root_dir" => "0-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1170 …2} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1171 …2} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1172 …2} "field_content_source" => null ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "task" => array:2 [ "refs" => "1108651" "type" => "task" ] "text" => "<p><strong>896.</strong> Упростите выражение и найдите его значение:</p><p><strong>а)</strong> $(\frac{1}{a+3} - \frac{6}{9-a^2}) \cdot (\frac{a-3}{a^2+9} + \frac{6a}{a^3-3a^2+9a-27})$ при $a = \frac{1}{7}$;</p><p><strong>б)</strong> $\frac{3b+2}{3b-2} : (\frac{18b}{27b^3-8} + \frac{6b}{9b^2+6b+4} - \frac{1}{3b-2}) - \frac{6b+8}{3b-2}$ при $b = -2\frac{1}{6}$;</p><p><strong>в)</strong> $\frac{a^2-b^2}{a-b} - \frac{a^3-b^3}{a^2-b^2}$, если $a = 3^{-1}, b = 7^{-1}$;</p><p><strong>г)</strong> $\frac{(a+b)^{-1}+(a-b)^{-1}}{(a+b)^{-1}-(a-b)^{-1}}$, если $a = \sqrt{27}, b = \sqrt{48}$.</p>" "img" => array:1 [ 0 => array:5 [ "name" => "896-1.jpg" "alt" => null "width" => "1573" "height" => 788 "path" => "/media/algebra_09/soltan-u19/0-1/896-1.webp?ts=1752834875" ] ] ] #original: array:7 [ "id" => 1277251 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1175} "task" => array:2 [ "refs" => "1108651" "type" => "task" ] "text" => "<p><strong>896.</strong> Упростите выражение и найдите его значение:</p><p><strong>а)</strong> $(\frac{1}{a+3} - \frac{6}{9-a^2}) \cdot (\frac{a-3}{a^2+9} + \frac{6a}{a^3-3a^2+9a-27})$ при $a = \frac{1}{7}$;</p><p><strong>б)</strong> $\frac{3b+2}{3b-2} : (\frac{18b}{27b^3-8} + \frac{6b}{9b^2+6b+4} - \frac{1}{3b-2}) - \frac{6b+8}{3b-2}$ при $b = -2\frac{1}{6}$;</p><p><strong>в)</strong> $\frac{a^2-b^2}{a-b} - \frac{a^3-b^3}{a^2-b^2}$, если $a = 3^{-1}, b = 7^{-1}$;</p><p><strong>г)</strong> $\frac{(a+b)^{-1}+(a-b)^{-1}}{(a+b)^{-1}-(a-b)^{-1}}$, если $a = \sqrt{27}, b = \sqrt{48}$.</p>" "img" => array:1 [ 0 => array:5 [ "name" => "896-1.jpg" "alt" => null "width" => "1573" "height" => 788 "path" => "/media/algebra_09/soltan-u19/0-1/896-1.webp?ts=1752834875" ] ] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 1 => App\Models\Element {#1173 #connection: "mysql" #table: "elements" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 1278542 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1183 #items: array:1 [ 0 => App\Models\Edition {#1174 #connection: "mysql" #table: "editions" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:21 [ "id" => 4954 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Решение" "field_order" => "2" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1177 …2} "field_content_type" => "free" "field_content_mode" => "image" "field_page_content_mode" => "" "field_content_text_checked" => "0" "field_page_content_text_checked" => "0" "field_solution_author" => "Неизвестный" "field_moderator" => "pasha" "field_edition_type" => "solution" "field_root_dir" => "1-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1178 …2} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1179 …2} "field_process_formula" => "" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1180 …2} "field_content_source" => null ] #original: array:21 [ "id" => 4954 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Решение" "field_order" => "2" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1177 …2} "field_content_type" => "free" "field_content_mode" => "image" "field_page_content_mode" => "" "field_content_text_checked" => "0" "field_page_content_text_checked" => "0" "field_solution_author" => "Неизвестный" "field_moderator" => "pasha" "field_edition_type" => "solution" "field_root_dir" => "1-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1178 …2} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1179 …2} "field_process_formula" => "" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1180 …2} "field_content_source" => null ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "task" => array:2 [ "refs" => "1108651" "type" => "task" ] "img" => array:3 [ 0 => array:5 [ "name" => "896-1.jpg" "alt" => null "width" => "1379" "height" => 1421 "path" => "/media/algebra_09/soltan-u19/1-1/896-1.webp?ts=1752831710" ] 1 => array:5 [ "name" => "896-2.jpg" "alt" => null "width" => "1394" "height" => 2444 "path" => "/media/algebra_09/soltan-u19/1-1/896-2.webp?ts=1752831710" ] 2 => array:5 [ "name" => "896-3.jpg" "alt" => null "width" => "1124" "height" => 1353 "path" => "/media/algebra_09/soltan-u19/1-1/896-3.webp?ts=1752831710" ] ] ] #original: array:6 [ "id" => 1278542 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1183} "task" => array:2 [ "refs" => "1108651" "type" => "task" ] "img" => array:3 [ 0 => array:5 [ "name" => "896-1.jpg" "alt" => null "width" => "1379" "height" => 1421 "path" => "/media/algebra_09/soltan-u19/1-1/896-1.webp?ts=1752831710" ] 1 => array:5 [ "name" => "896-2.jpg" "alt" => null "width" => "1394" "height" => 2444 "path" => "/media/algebra_09/soltan-u19/1-1/896-2.webp?ts=1752831710" ] 2 => array:5 [ "name" => "896-3.jpg" "alt" => null "width" => "1124" "height" => 1353 "path" => "/media/algebra_09/soltan-u19/1-1/896-3.webp?ts=1752831710" ] ] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 2 => App\Models\Element {#1181 #connection: "mysql" #table: "elements" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 1554497 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1191 #items: array:1 [ 0 => App\Models\Edition {#1182 #connection: "mysql" #table: "editions" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:21 [ "id" => 5665 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Решение 2 (rus)" "field_order" => "3" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1185 …2} "field_content_type" => "free" "field_content_mode" => "text" "field_page_content_mode" => "" "field_content_text_checked" => null "field_page_content_text_checked" => "0" "field_solution_author" => "Gemini 2.5 Pro" "field_moderator" => "tolik" "field_edition_type" => "solution" "field_root_dir" => "2-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1186 …2} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1187 …2} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1188 …2} "field_content_source" => null ] #original: array:21 [ "id" => 5665 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Решение 2 (rus)" "field_order" => "3" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1185 …2} "field_content_type" => "free" "field_content_mode" => "text" "field_page_content_mode" => "" "field_content_text_checked" => null "field_page_content_text_checked" => "0" "field_solution_author" => "Gemini 2.5 Pro" "field_moderator" => "tolik" "field_edition_type" => "solution" "field_root_dir" => "2-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1186 …2} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1187 …2} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1188 …2} "field_content_source" => null ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "task" => array:2 [ "refs" => "1108651" "type" => "task" ] "text" => "<p><strong>а)</strong></p><p>Сначала упростим выражение по действиям.</p><p>1) Упростим выражение в первой скобке. Приведем дроби к общему знаменателю, разложив знаменатель второй дроби по формуле разности квадратов $9-a^2 = (3-a)(3+a) = -(a-3)(a+3)$.</p><p>$\frac{1}{a+3} - \frac{6}{9-a^2} = \frac{1}{a+3} + \frac{6}{a^2-9} = \frac{1}{a+3} + \frac{6}{(a-3)(a+3)} = \frac{1 \cdot (a-3)}{(a-3)(a+3)} + \frac{6}{(a-3)(a+3)} = \frac{a-3+6}{(a-3)(a+3)} = \frac{a+3}{(a-3)(a+3)} = \frac{1}{a-3}.$</p><p>2) Упростим выражение во второй скобке. Разложим знаменатель второй дроби на множители методом группировки: $a^3-3a^2+9a-27 = a^2(a-3)+9(a-3) = (a-3)(a^2+9)$.</p><p>$\frac{a-3}{a^2+9} + \frac{6a}{a^3-3a^2+9a-27} = \frac{a-3}{a^2+9} + \frac{6a}{(a-3)(a^2+9)} = \frac{(a-3)(a-3)}{(a-3)(a^2+9)} + \frac{6a}{(a-3)(a^2+9)} = \frac{a^2-6a+9+6a}{(a-3)(a^2+9)} = \frac{a^2+9}{(a-3)(a^2+9)} = \frac{1}{a-3}.$</p><p>3) Перемножим результаты, полученные в пунктах 1 и 2.</p><p>$\frac{1}{a-3} \cdot \frac{1}{a-3} = \frac{1}{(a-3)^2}.$</p><p>4) Теперь подставим значение $a = \frac{1}{7}$ в упрощенное выражение.</p><p>$\frac{1}{(\frac{1}{7}-3)^2} = \frac{1}{(\frac{1-21}{7})^2} = \frac{1}{(-\frac{20}{7})^2} = \frac{1}{\frac{400}{49}} = \frac{49}{400}.$</p><p><strong>Ответ:</strong> $\frac{49}{400}.$</p><p><strong>б)</strong></p><p>Сначала упростим выражение по действиям.</p><p>1) Выполним действия в скобках. Разложим знаменатель первой дроби по формуле разности кубов: $27b^3-8 = (3b)^3 - 2^3 = (3b-2)(9b^2+6b+4)$.</p><p>$(\frac{18b}{(3b-2)(9b^2+6b+4)} + \frac{6b}{9b^2+6b+4} - \frac{1}{3b-2}) = \frac{18b + 6b(3b-2) - 1(9b^2+6b+4)}{(3b-2)(9b^2+6b+4)} = \frac{18b + 18b^2 - 12b - 9b^2 - 6b - 4}{(3b-2)(9b^2+6b+4)} = \frac{9b^2-4}{(3b-2)(9b^2+6b+4)}.$</p><p>Разложим числитель по формуле разности квадратов: $9b^2-4 = (3b-2)(3b+2)$.</p><p>$\frac{(3b-2)(3b+2)}{(3b-2)(9b^2+6b+4)} = \frac{3b+2}{9b^2+6b+4}.$</p><p>2) Выполним деление.</p><p>$\frac{3b+2}{3b-2} : \frac{3b+2}{9b^2+6b+4} = \frac{3b+2}{3b-2} \cdot \frac{9b^2+6b+4}{3b+2} = \frac{9b^2+6b+4}{3b-2}.$</p><p>3) Выполним вычитание.</p><p>$\frac{9b^2+6b+4}{3b-2} - \frac{6b+8}{3b-2} = \frac{9b^2+6b+4 - (6b+8)}{3b-2} = \frac{9b^2+6b+4-6b-8}{3b-2} = \frac{9b^2-4}{3b-2} = \frac{(3b-2)(3b+2)}{3b-2} = 3b+2.$</p><p>4) Теперь подставим значение $b = -2\frac{1}{6}$ в упрощенное выражение. Сначала переведем смешанное число в неправильную дробь: $b = -2\frac{1}{6} = -\frac{12+1}{6} = -\frac{13}{6}$.</p><p>$3b+2 = 3 \cdot (-\frac{13}{6}) + 2 = -\frac{13}{2} + 2 = -6.5 + 2 = -4.5.$</p><p><strong>Ответ:</strong> $-4.5.$</p><p><strong>в)</strong></p><p>Сначала упростим выражение, используя формулы сокращенного умножения: разность квадратов $a^2-b^2=(a-b)(a+b)$ и разность кубов $a^3-b^3=(a-b)(a^2+ab+b^2)$.</p><p>$\frac{a^2-b^2}{a-b} - \frac{a^3-b^3}{a^2-b^2} = \frac{(a-b)(a+b)}{a-b} - \frac{(a-b)(a^2+ab+b^2)}{(a-b)(a+b)} = (a+b) - \frac{a^2+ab+b^2}{a+b}.$</p><p>Приведем к общему знаменателю:</p><p>$\frac{(a+b)(a+b)}{a+b} - \frac{a^2+ab+b^2}{a+b} = \frac{(a+b)^2 - (a^2+ab+b^2)}{a+b} = \frac{a^2+2ab+b^2 - a^2-ab-b^2}{a+b} = \frac{ab}{a+b}.$</p><p>Теперь найдем значения $a$ и $b$: $a = 3^{-1} = \frac{1}{3}$ и $b = 7^{-1} = \frac{1}{7}$.</p><p>Подставим эти значения в упрощенное выражение.</p><p>$\frac{\frac{1}{3} \cdot \frac{1}{7}}{\frac{1}{3} + \frac{1}{7}} = \frac{\frac{1}{21}}{\frac{7+3}{21}} = \frac{\frac{1}{21}}{\frac{10}{21}} = \frac{1}{21} \cdot \frac{21}{10} = \frac{1}{10}.$</p><p><strong>Ответ:</strong> $\frac{1}{10}.$</p><p><strong>г)</strong></p><p>Сначала упростим выражение. Используем свойство $x^{-1} = \frac{1}{x}$.</p><p>$\frac{(a+b)^{-1}+(a-b)^{-1}}{(a+b)^{-1}-(a-b)^{-1}} = \frac{\frac{1}{a+b}+\frac{1}{a-b}}{\frac{1}{a+b}-\frac{1}{a-b}}.$</p><p>Упростим числитель и знаменатель основной дроби, приведя дроби в них к общему знаменателю $(a+b)(a-b)=a^2-b^2$.</p><p>Числитель: $\frac{1}{a+b}+\frac{1}{a-b} = \frac{a-b+a+b}{(a+b)(a-b)} = \frac{2a}{a^2-b^2}.$</p><p>Знаменатель: $\frac{1}{a+b}-\frac{1}{a-b} = \frac{a-b-(a+b)}{(a+b)(a-b)} = \frac{a-b-a-b}{a^2-b^2} = \frac{-2b}{a^2-b^2}.$</p><p>Теперь разделим числитель на знаменатель:</p><p>$\frac{\frac{2a}{a^2-b^2}}{\frac{-2b}{a^2-b^2}} = \frac{2a}{a^2-b^2} \cdot \frac{a^2-b^2}{-2b} = \frac{2a}{-2b} = -\frac{a}{b}.$</p><p>Найдем значения $a$ и $b$: $a = \sqrt{27} = \sqrt{9 \cdot 3} = 3\sqrt{3}$ и $b = \sqrt{48} = \sqrt{16 \cdot 3} = 4\sqrt{3}$.</p><p>Подставим эти значения в упрощенное выражение.</p><p>$-\frac{a}{b} = -\frac{3\sqrt{3}}{4\sqrt{3}} = -\frac{3}{4}.$</p><p><strong>Ответ:</strong> $-\frac{3}{4}.$</p>" ] #original: array:6 [ "id" => 1554497 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1191} "task" => array:2 [ "refs" => "1108651" "type" => "task" ] "text" => "<p><strong>а)</strong></p><p>Сначала упростим выражение по действиям.</p><p>1) Упростим выражение в первой скобке. Приведем дроби к общему знаменателю, разложив знаменатель второй дроби по формуле разности квадратов $9-a^2 = (3-a)(3+a) = -(a-3)(a+3)$.</p><p>$\frac{1}{a+3} - \frac{6}{9-a^2} = \frac{1}{a+3} + \frac{6}{a^2-9} = \frac{1}{a+3} + \frac{6}{(a-3)(a+3)} = \frac{1 \cdot (a-3)}{(a-3)(a+3)} + \frac{6}{(a-3)(a+3)} = \frac{a-3+6}{(a-3)(a+3)} = \frac{a+3}{(a-3)(a+3)} = \frac{1}{a-3}.$</p><p>2) Упростим выражение во второй скобке. Разложим знаменатель второй дроби на множители методом группировки: $a^3-3a^2+9a-27 = a^2(a-3)+9(a-3) = (a-3)(a^2+9)$.</p><p>$\frac{a-3}{a^2+9} + \frac{6a}{a^3-3a^2+9a-27} = \frac{a-3}{a^2+9} + \frac{6a}{(a-3)(a^2+9)} = \frac{(a-3)(a-3)}{(a-3)(a^2+9)} + \frac{6a}{(a-3)(a^2+9)} = \frac{a^2-6a+9+6a}{(a-3)(a^2+9)} = \frac{a^2+9}{(a-3)(a^2+9)} = \frac{1}{a-3}.$</p><p>3) Перемножим результаты, полученные в пунктах 1 и 2.</p><p>$\frac{1}{a-3} \cdot \frac{1}{a-3} = \frac{1}{(a-3)^2}.$</p><p>4) Теперь подставим значение $a = \frac{1}{7}$ в упрощенное выражение.</p><p>$\frac{1}{(\frac{1}{7}-3)^2} = \frac{1}{(\frac{1-21}{7})^2} = \frac{1}{(-\frac{20}{7})^2} = \frac{1}{\frac{400}{49}} = \frac{49}{400}.$</p><p><strong>Ответ:</strong> $\frac{49}{400}.$</p><p><strong>б)</strong></p><p>Сначала упростим выражение по действиям.</p><p>1) Выполним действия в скобках. Разложим знаменатель первой дроби по формуле разности кубов: $27b^3-8 = (3b)^3 - 2^3 = (3b-2)(9b^2+6b+4)$.</p><p>$(\frac{18b}{(3b-2)(9b^2+6b+4)} + \frac{6b}{9b^2+6b+4} - \frac{1}{3b-2}) = \frac{18b + 6b(3b-2) - 1(9b^2+6b+4)}{(3b-2)(9b^2+6b+4)} = \frac{18b + 18b^2 - 12b - 9b^2 - 6b - 4}{(3b-2)(9b^2+6b+4)} = \frac{9b^2-4}{(3b-2)(9b^2+6b+4)}.$</p><p>Разложим числитель по формуле разности квадратов: $9b^2-4 = (3b-2)(3b+2)$.</p><p>$\frac{(3b-2)(3b+2)}{(3b-2)(9b^2+6b+4)} = \frac{3b+2}{9b^2+6b+4}.$</p><p>2) Выполним деление.</p><p>$\frac{3b+2}{3b-2} : \frac{3b+2}{9b^2+6b+4} = \frac{3b+2}{3b-2} \cdot \frac{9b^2+6b+4}{3b+2} = \frac{9b^2+6b+4}{3b-2}.$</p><p>3) Выполним вычитание.</p><p>$\frac{9b^2+6b+4}{3b-2} - \frac{6b+8}{3b-2} = \frac{9b^2+6b+4 - (6b+8)}{3b-2} = \frac{9b^2+6b+4-6b-8}{3b-2} = \frac{9b^2-4}{3b-2} = \frac{(3b-2)(3b+2)}{3b-2} = 3b+2.$</p><p>4) Теперь подставим значение $b = -2\frac{1}{6}$ в упрощенное выражение. Сначала переведем смешанное число в неправильную дробь: $b = -2\frac{1}{6} = -\frac{12+1}{6} = -\frac{13}{6}$.</p><p>$3b+2 = 3 \cdot (-\frac{13}{6}) + 2 = -\frac{13}{2} + 2 = -6.5 + 2 = -4.5.$</p><p><strong>Ответ:</strong> $-4.5.$</p><p><strong>в)</strong></p><p>Сначала упростим выражение, используя формулы сокращенного умножения: разность квадратов $a^2-b^2=(a-b)(a+b)$ и разность кубов $a^3-b^3=(a-b)(a^2+ab+b^2)$.</p><p>$\frac{a^2-b^2}{a-b} - \frac{a^3-b^3}{a^2-b^2} = \frac{(a-b)(a+b)}{a-b} - \frac{(a-b)(a^2+ab+b^2)}{(a-b)(a+b)} = (a+b) - \frac{a^2+ab+b^2}{a+b}.$</p><p>Приведем к общему знаменателю:</p><p>$\frac{(a+b)(a+b)}{a+b} - \frac{a^2+ab+b^2}{a+b} = \frac{(a+b)^2 - (a^2+ab+b^2)}{a+b} = \frac{a^2+2ab+b^2 - a^2-ab-b^2}{a+b} = \frac{ab}{a+b}.$</p><p>Теперь найдем значения $a$ и $b$: $a = 3^{-1} = \frac{1}{3}$ и $b = 7^{-1} = \frac{1}{7}$.</p><p>Подставим эти значения в упрощенное выражение.</p><p>$\frac{\frac{1}{3} \cdot \frac{1}{7}}{\frac{1}{3} + \frac{1}{7}} = \frac{\frac{1}{21}}{\frac{7+3}{21}} = \frac{\frac{1}{21}}{\frac{10}{21}} = \frac{1}{21} \cdot \frac{21}{10} = \frac{1}{10}.$</p><p><strong>Ответ:</strong> $\frac{1}{10}.$</p><p><strong>г)</strong></p><p>Сначала упростим выражение. Используем свойство $x^{-1} = \frac{1}{x}$.</p><p>$\frac{(a+b)^{-1}+(a-b)^{-1}}{(a+b)^{-1}-(a-b)^{-1}} = \frac{\frac{1}{a+b}+\frac{1}{a-b}}{\frac{1}{a+b}-\frac{1}{a-b}}.$</p><p>Упростим числитель и знаменатель основной дроби, приведя дроби в них к общему знаменателю $(a+b)(a-b)=a^2-b^2$.</p><p>Числитель: $\frac{1}{a+b}+\frac{1}{a-b} = \frac{a-b+a+b}{(a+b)(a-b)} = \frac{2a}{a^2-b^2}.$</p><p>Знаменатель: $\frac{1}{a+b}-\frac{1}{a-b} = \frac{a-b-(a+b)}{(a+b)(a-b)} = \frac{a-b-a-b}{a^2-b^2} = \frac{-2b}{a^2-b^2}.$</p><p>Теперь разделим числитель на знаменатель:</p><p>$\frac{\frac{2a}{a^2-b^2}}{\frac{-2b}{a^2-b^2}} = \frac{2a}{a^2-b^2} \cdot \frac{a^2-b^2}{-2b} = \frac{2a}{-2b} = -\frac{a}{b}.$</p><p>Найдем значения $a$ и $b$: $a = \sqrt{27} = \sqrt{9 \cdot 3} = 3\sqrt{3}$ и $b = \sqrt{48} = \sqrt{16 \cdot 3} = 4\sqrt{3}$.</p><p>Подставим эти значения в упрощенное выражение.</p><p>$-\frac{a}{b} = -\frac{3\sqrt{3}}{4\sqrt{3}} = -\frac{3}{4}.$</p><p><strong>Ответ:</strong> $-\frac{3}{4}.$</p>" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "next" => array:2 [ "refs" => "1108652" "type" => "task" ] "previous" => array:2 [ "refs" => "1108650" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1195 #items: array:1 [ 0 => App\Models\Book {#1163 #connection: "mysql" #table: "books" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:50 [ "id" => 4298 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_tree_default_status" => "tasks" "field_pages_status" => null "field_subject" => Illuminate\Database\Eloquent\Collection {#1148 #items: array:1 [ 0 => App\Models\Term {#1147 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:10 [ "id" => 6471 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Алгебра" "field_abbreviated_name" => null "field_cases" => array:6 [ …6] "field_foreign_lang_name" => null "field_short_name" => null "field_subject_type" => "technical_subject" "field_translit" => "algebra" ] #original: array:10 [ "id" => 6471 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Алгебра" "field_abbreviated_name" => null "field_cases" => array:6 [ …6] "field_foreign_lang_name" => null "field_short_name" => null "field_subject_type" => "technical_subject" "field_translit" => "algebra" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_class" => Illuminate\Database\Eloquent\Collection {#1149 #items: array:1 [ 0 => App\Models\Term {#1154 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 5458 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "9" "field_cases" => array:6 [ …6] "field_translit" => "devjatyj" ] #original: array:6 [ "id" => 5458 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "9" "field_cases" => array:6 [ …6] "field_translit" => "devjatyj" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_publisher" => Illuminate\Database\Eloquent\Collection {#1153 #items: array:1 [ 0 => App\Models\Term {#1152 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 7002 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Кокшетау" "field_cases" => array:6 [ …6] "field_translit" => "Kokshetau" ] #original: array:6 [ "id" => 7002 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Кокшетау" "field_cases" => array:6 [ …6] "field_translit" => "Kokshetau" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_author" => Illuminate\Database\Eloquent\Collection {#1150 #items: array:3 [ 0 => App\Models\Term {#1151 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:12 [ "id" => 7003 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Солтан" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Генадий" "field_patronymic" => "Николаевич" "field_surname_rp" => null ] #original: array:12 [ "id" => 7003 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Солтан" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Генадий" "field_patronymic" => "Николаевич" "field_surname_rp" => null ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 1 => App\Models\Term {#1140 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:12 [ "id" => 7004 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Солтан" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Алла" "field_patronymic" => "Евгеньевна" "field_surname_rp" => null ] #original: array:12 [ "id" => 7004 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Солтан" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Алла" "field_patronymic" => "Евгеньевна" "field_surname_rp" => null ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 2 => App\Models\Term {#1141 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:12 [ "id" => 7005 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Жумадилова" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Аманбала" "field_patronymic" => "Жумадиловна" "field_surname_rp" => null ] #original: array:12 [ "id" => 7005 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Жумадилова" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Аманбала" "field_patronymic" => "Жумадиловна" "field_surname_rp" => null ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1139 #items: [] #escapeWhenCastingToString: false } "field_book_type" => Illuminate\Database\Eloquent\Collection {#1146 #items: array:1 [ 0 => App\Models\Term {#1145 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:10 [ "id" => 6671 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Учебник" "field_book_type_foreign" => null "field_cases" => array:6 [ …6] "field_plural_form" => null "field_short_name" => null "field_short_name_foreign" => null "field_translit" => "uchebnik" ] #original: array:10 [ "id" => 6671 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Учебник" "field_book_type_foreign" => null "field_cases" => array:6 [ …6] "field_plural_form" => null "field_short_name" => null "field_short_name_foreign" => null "field_translit" => "uchebnik" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_country" => Illuminate\Database\Eloquent\Collection {#1144 #items: array:1 [ 0 => App\Models\Term {#1142 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 6994 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Казахстан" "field_cases" => array:6 [ …6] "field_translit" => "kazakhstan" ] #original: array:6 [ "id" => 6994 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Казахстан" "field_cases" => array:6 [ …6] "field_translit" => "kazakhstan" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_city" => Illuminate\Database\Eloquent\Collection {#1143 #items: array:1 [ 0 => App\Models\Term {#1157 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 6995 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Алматы" "field_cases" => array:6 [ …6] "field_translit" => "almaty" ] #original: array:6 [ "id" => 6995 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Алматы" "field_cases" => array:6 [ …6] "field_translit" => "almaty" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_series" => Illuminate\Database\Eloquent\Collection {#1155 #items: [] #escapeWhenCastingToString: false } "field_umk" => Illuminate\Database\Eloquent\Collection {#1162 #items: [] #escapeWhenCastingToString: false } "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1164 #items: [] #escapeWhenCastingToString: false } "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1160 #items: [] #escapeWhenCastingToString: false } "field_publication_number" => null "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1158 #items: [] #escapeWhenCastingToString: false } "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1161 #items: [] #escapeWhenCastingToString: false } "field_under_the_edition_degree" => null "field_cover_description" => null "field_publication_year" => "2019" "field_publication_year_until" => null "field_part" => "" "field_part_writing" => "" "field_second_foreign_language" => null "field_for_whom" => "Учебник для учащихся 9 класса общеобразовательных школ" "field_allowed" => "Рекомендовано Министерством образования и науки Республики Казахстан" "field_reserve_field" => null "field_link_to_source" => null "field_tasks_count" => "1291" "field_priority" => "4" "field_default_folder" => "/algebra_09/soltan-u19/" "field_isbn" => "978-601-317-424-2" "field_cover" => array:1 [ 0 => "/media/algebra_09/soltan-u19/covers/cover1.webp?ts=1752140452" ] "field_cover_alts" => array:1 [ 0 => "" ] "field_covers" => array:1 [ 0 => array:4 [ "path" => "/media/algebra_09/soltan-u19/covers/cover1.webp?ts=1752140452" "alt" => "" "width" => "1940" "height" => "2895" ] ] "field_popular_book" => null "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1159 #items: [] #escapeWhenCastingToString: false } "field_new_book" => Illuminate\Database\Eloquent\Collection {#1189 #items: [] #escapeWhenCastingToString: false } "field_old_book" => Illuminate\Database\Eloquent\Collection {#1190 #items: [] #escapeWhenCastingToString: false } "field_url" => "/9-klass/algebra/kokshetau-soltan-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1192 #items: [] #escapeWhenCastingToString: false } "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "breadcrumbs" => array:3 [ "class" => 380 "subject" => 542 "class_subject" => 386 ] ] #original: array:50 [ "id" => 4298 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_tree_default_status" => "tasks" "field_pages_status" => null "field_subject" => Illuminate\Database\Eloquent\Collection {#1148} "field_class" => Illuminate\Database\Eloquent\Collection {#1149} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1153} "field_author" => Illuminate\Database\Eloquent\Collection {#1150} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1139} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1146} "field_country" => Illuminate\Database\Eloquent\Collection {#1144} "field_city" => Illuminate\Database\Eloquent\Collection {#1143} "field_series" => Illuminate\Database\Eloquent\Collection {#1155} "field_umk" => Illuminate\Database\Eloquent\Collection {#1162} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1164} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1160} "field_publication_number" => null "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1158} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1161} "field_under_the_edition_degree" => null "field_cover_description" => null "field_publication_year" => "2019" "field_publication_year_until" => null "field_part" => "" "field_part_writing" => "" "field_second_foreign_language" => null "field_for_whom" => "Учебник для учащихся 9 класса общеобразовательных школ" "field_allowed" => "Рекомендовано Министерством образования и науки Республики Казахстан" "field_reserve_field" => null "field_link_to_source" => null "field_tasks_count" => "1291" "field_priority" => "4" "field_default_folder" => "/algebra_09/soltan-u19/" "field_isbn" => "978-601-317-424-2" "field_cover" => array:1 [ 0 => "/media/algebra_09/soltan-u19/covers/cover1.webp?ts=1752140452" ] "field_cover_alts" => array:1 [ 0 => "" ] "field_covers" => array:1 [ 0 => array:4 [ "path" => "/media/algebra_09/soltan-u19/covers/cover1.webp?ts=1752140452" "alt" => "" "width" => "1940" "height" => "2895" ] ] "field_popular_book" => null "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1159} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1189} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1190} "field_url" => "/9-klass/algebra/kokshetau-soltan-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1192} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "breadcrumbs" => array:3 [ "class" => 380 "subject" => 542 "class_subject" => 386 ] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "page" => Illuminate\Database\Eloquent\Collection {#1200 #items: array:1 [ 0 => App\Models\BookPage {#1199 #connection: "mysql" #table: "book_pages" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:21 [ "id" => 1097991 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "249" "field_url" => "/9-klass/algebra/kokshetau-soltan-uchebnik/page-249" "field_display_title" => "249" "field_folder" => "folder1" "field_image_name" => "249" "field_branch_parent" => Illuminate\Database\Eloquent\Collection {#1201 #items: [] #escapeWhenCastingToString: false } "field_weight" => "0" "field_book_parent" => Illuminate\Database\Eloquent\Collection {#1202 #items: array:1 [ 0 => App\Models\Book {#1163} ] #escapeWhenCastingToString: false } "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "edition_groups" => Illuminate\Database\Eloquent\Collection {#1203 #items: [] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1213 #items: array:1 [ 0 => App\Models\Element {#1212 #connection: "mysql" #table: "elements" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 1261142 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1214 …2} "book_page" => array:2 [ …2] "img" => array:1 [ …1] ] #original: array:6 [ "id" => 1261142 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1214 …2} "book_page" => array:2 [ …2] "img" => array:1 [ …1] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "next" => array:2 [ "refs" => "1097992" "type" => "book_page" ] "previous" => array:2 [ "refs" => "1097990" "type" => "book_page" ] "tasks" => Illuminate\Database\Eloquent\Collection {#1667 #items: array:6 [ 0 => App\Models\Task {#1679 #connection: "mysql" #table: "tasks" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ "id" => 1108648 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "249" "field_page_end" => null "field_url" => "/9-klass/algebra/kokshetau-soltan-uchebnik/1-893" "field_display_title" => "893" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1680 …2} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#1681 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1682 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1683 …2} "content" => Illuminate\Database\Eloquent\Collection {#1701 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1708 …2} "page" => array:2 [ …2] ] #original: array:24 [ "id" => 1108648 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "249" "field_page_end" => null "field_url" => "/9-klass/algebra/kokshetau-soltan-uchebnik/1-893" "field_display_title" => "893" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1680 …2} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#1681 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1682 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1683 …2} "content" => Illuminate\Database\Eloquent\Collection {#1701 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1708 …2} "page" => array:2 [ …2] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 1 => App\Models\Task {#1692 #connection: "mysql" #table: "tasks" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ "id" => 1108649 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "249" "field_page_end" => null "field_url" => "/9-klass/algebra/kokshetau-soltan-uchebnik/1-894" "field_display_title" => "894" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1693 …2} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#1694 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1699 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1698 …2} "content" => Illuminate\Database\Eloquent\Collection {#1706 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1722 …2} "page" => array:2 [ …2] ] #original: array:24 [ "id" => 1108649 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "249" "field_page_end" => null "field_url" => "/9-klass/algebra/kokshetau-soltan-uchebnik/1-894" "field_display_title" => "894" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1693 …2} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#1694 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1699 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1698 …2} "content" => Illuminate\Database\Eloquent\Collection {#1706 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1722 …2} "page" => array:2 [ …2] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 2 => App\Models\Task {#1689 #connection: "mysql" #table: "tasks" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ "id" => 1108650 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "249" "field_page_end" => null "field_url" => "/9-klass/algebra/kokshetau-soltan-uchebnik/1-895" "field_display_title" => "895" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1687 …2} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#1688 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1705 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1709 …2} "content" => Illuminate\Database\Eloquent\Collection {#1720 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1736 …2} "page" => array:2 [ …2] ] #original: array:24 [ "id" => 1108650 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "249" "field_page_end" => null "field_url" => "/9-klass/algebra/kokshetau-soltan-uchebnik/1-895" "field_display_title" => "895" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1687 …2} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#1688 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1705 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1709 …2} "content" => Illuminate\Database\Eloquent\Collection {#1720 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1736 …2} "page" => array:2 [ …2] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 3 => App\Models\Task {#1685 #connection: "mysql" #table: "tasks" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ "id" => 1108651 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "249" "field_page_end" => null "field_url" => "/9-klass/algebra/kokshetau-soltan-uchebnik/1-896" "field_display_title" => "896" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1684 …2} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => 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№896 (с. 249)
Условие. №896 (с. 249)
скриншот условия
896. Упростите выражение и найдите его значение:
а) $(\frac{1}{a+3} - \frac{6}{9-a^2}) \cdot (\frac{a-3}{a^2+9} + \frac{6a}{a^3-3a^2+9a-27})$ при $a = \frac{1}{7}$;
б) $\frac{3b+2}{3b-2} : (\frac{18b}{27b^3-8} + \frac{6b}{9b^2+6b+4} - \frac{1}{3b-2}) - \frac{6b+8}{3b-2}$ при $b = -2\frac{1}{6}$;
в) $\frac{a^2-b^2}{a-b} - \frac{a^3-b^3}{a^2-b^2}$, если $a = 3^{-1}, b = 7^{-1}$;
г) $\frac{(a+b)^{-1}+(a-b)^{-1}}{(a+b)^{-1}-(a-b)^{-1}}$, если $a = \sqrt{27}, b = \sqrt{48}$.
Решение. №896 (с. 249)
Решение 2 (rus). №896 (с. 249)
а)
Сначала упростим выражение по действиям.
1) Упростим выражение в первой скобке. Приведем дроби к общему знаменателю, разложив знаменатель второй дроби по формуле разности квадратов $9-a^2 = (3-a)(3+a) = -(a-3)(a+3)$.
$\frac{1}{a+3} - \frac{6}{9-a^2} = \frac{1}{a+3} + \frac{6}{a^2-9} = \frac{1}{a+3} + \frac{6}{(a-3)(a+3)} = \frac{1 \cdot (a-3)}{(a-3)(a+3)} + \frac{6}{(a-3)(a+3)} = \frac{a-3+6}{(a-3)(a+3)} = \frac{a+3}{(a-3)(a+3)} = \frac{1}{a-3}.$
2) Упростим выражение во второй скобке. Разложим знаменатель второй дроби на множители методом группировки: $a^3-3a^2+9a-27 = a^2(a-3)+9(a-3) = (a-3)(a^2+9)$.
$\frac{a-3}{a^2+9} + \frac{6a}{a^3-3a^2+9a-27} = \frac{a-3}{a^2+9} + \frac{6a}{(a-3)(a^2+9)} = \frac{(a-3)(a-3)}{(a-3)(a^2+9)} + \frac{6a}{(a-3)(a^2+9)} = \frac{a^2-6a+9+6a}{(a-3)(a^2+9)} = \frac{a^2+9}{(a-3)(a^2+9)} = \frac{1}{a-3}.$
3) Перемножим результаты, полученные в пунктах 1 и 2.
$\frac{1}{a-3} \cdot \frac{1}{a-3} = \frac{1}{(a-3)^2}.$
4) Теперь подставим значение $a = \frac{1}{7}$ в упрощенное выражение.
$\frac{1}{(\frac{1}{7}-3)^2} = \frac{1}{(\frac{1-21}{7})^2} = \frac{1}{(-\frac{20}{7})^2} = \frac{1}{\frac{400}{49}} = \frac{49}{400}.$
Ответ: $\frac{49}{400}.$
б)
Сначала упростим выражение по действиям.
1) Выполним действия в скобках. Разложим знаменатель первой дроби по формуле разности кубов: $27b^3-8 = (3b)^3 - 2^3 = (3b-2)(9b^2+6b+4)$.
$(\frac{18b}{(3b-2)(9b^2+6b+4)} + \frac{6b}{9b^2+6b+4} - \frac{1}{3b-2}) = \frac{18b + 6b(3b-2) - 1(9b^2+6b+4)}{(3b-2)(9b^2+6b+4)} = \frac{18b + 18b^2 - 12b - 9b^2 - 6b - 4}{(3b-2)(9b^2+6b+4)} = \frac{9b^2-4}{(3b-2)(9b^2+6b+4)}.$
Разложим числитель по формуле разности квадратов: $9b^2-4 = (3b-2)(3b+2)$.
$\frac{(3b-2)(3b+2)}{(3b-2)(9b^2+6b+4)} = \frac{3b+2}{9b^2+6b+4}.$
2) Выполним деление.
$\frac{3b+2}{3b-2} : \frac{3b+2}{9b^2+6b+4} = \frac{3b+2}{3b-2} \cdot \frac{9b^2+6b+4}{3b+2} = \frac{9b^2+6b+4}{3b-2}.$
3) Выполним вычитание.
$\frac{9b^2+6b+4}{3b-2} - \frac{6b+8}{3b-2} = \frac{9b^2+6b+4 - (6b+8)}{3b-2} = \frac{9b^2+6b+4-6b-8}{3b-2} = \frac{9b^2-4}{3b-2} = \frac{(3b-2)(3b+2)}{3b-2} = 3b+2.$
4) Теперь подставим значение $b = -2\frac{1}{6}$ в упрощенное выражение. Сначала переведем смешанное число в неправильную дробь: $b = -2\frac{1}{6} = -\frac{12+1}{6} = -\frac{13}{6}$.
$3b+2 = 3 \cdot (-\frac{13}{6}) + 2 = -\frac{13}{2} + 2 = -6.5 + 2 = -4.5.$
Ответ: $-4.5.$
в)
Сначала упростим выражение, используя формулы сокращенного умножения: разность квадратов $a^2-b^2=(a-b)(a+b)$ и разность кубов $a^3-b^3=(a-b)(a^2+ab+b^2)$.
$\frac{a^2-b^2}{a-b} - \frac{a^3-b^3}{a^2-b^2} = \frac{(a-b)(a+b)}{a-b} - \frac{(a-b)(a^2+ab+b^2)}{(a-b)(a+b)} = (a+b) - \frac{a^2+ab+b^2}{a+b}.$
Приведем к общему знаменателю:
$\frac{(a+b)(a+b)}{a+b} - \frac{a^2+ab+b^2}{a+b} = \frac{(a+b)^2 - (a^2+ab+b^2)}{a+b} = \frac{a^2+2ab+b^2 - a^2-ab-b^2}{a+b} = \frac{ab}{a+b}.$
Теперь найдем значения $a$ и $b$: $a = 3^{-1} = \frac{1}{3}$ и $b = 7^{-1} = \frac{1}{7}$.
Подставим эти значения в упрощенное выражение.
$\frac{\frac{1}{3} \cdot \frac{1}{7}}{\frac{1}{3} + \frac{1}{7}} = \frac{\frac{1}{21}}{\frac{7+3}{21}} = \frac{\frac{1}{21}}{\frac{10}{21}} = \frac{1}{21} \cdot \frac{21}{10} = \frac{1}{10}.$
Ответ: $\frac{1}{10}.$
г)
Сначала упростим выражение. Используем свойство $x^{-1} = \frac{1}{x}$.
$\frac{(a+b)^{-1}+(a-b)^{-1}}{(a+b)^{-1}-(a-b)^{-1}} = \frac{\frac{1}{a+b}+\frac{1}{a-b}}{\frac{1}{a+b}-\frac{1}{a-b}}.$
Упростим числитель и знаменатель основной дроби, приведя дроби в них к общему знаменателю $(a+b)(a-b)=a^2-b^2$.
Числитель: $\frac{1}{a+b}+\frac{1}{a-b} = \frac{a-b+a+b}{(a+b)(a-b)} = \frac{2a}{a^2-b^2}.$
Знаменатель: $\frac{1}{a+b}-\frac{1}{a-b} = \frac{a-b-(a+b)}{(a+b)(a-b)} = \frac{a-b-a-b}{a^2-b^2} = \frac{-2b}{a^2-b^2}.$
Теперь разделим числитель на знаменатель:
$\frac{\frac{2a}{a^2-b^2}}{\frac{-2b}{a^2-b^2}} = \frac{2a}{a^2-b^2} \cdot \frac{a^2-b^2}{-2b} = \frac{2a}{-2b} = -\frac{a}{b}.$
Найдем значения $a$ и $b$: $a = \sqrt{27} = \sqrt{9 \cdot 3} = 3\sqrt{3}$ и $b = \sqrt{48} = \sqrt{16 \cdot 3} = 4\sqrt{3}$.
Подставим эти значения в упрощенное выражение.
$-\frac{a}{b} = -\frac{3\sqrt{3}}{4\sqrt{3}} = -\frac{3}{4}.$
Ответ: $-\frac{3}{4}.$
Другие задания:
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