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Номер 93, страница 30 - гдз по алгебре 8 класс учебник Дорофеев, Суворова
Авторы: Дорофеев Г. В., Суворова С. Б., Бунимович Е. А., Кузнецова Л. В., Минаева С. С., Рослова Л. О.
Тип: Учебник
Издательство: Просвещение
Год издания: 2019 - 2022
Цвет обложки: белый, бирюзовый, оранжевый
Допущено Министерством просвещения Российской Федерации
Популярные ГДЗ в 8 классе
Глава 1. Алгебраические дроби. 1.5. Преобразование выражений, содержащих алгебраические дроби - номер 93, страница 30.
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" => 209102 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "30" "field_page_end" => null "field_url" => "/8-klass/algebra/dorofeev-uchebnik/93" "field_display_title" => "93" "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 {#1046 #items: array:1 [ 0 => App\Models\Branch {#1045 #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" => 208891 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Алгебраические дроби" "field_branch_order" => "1" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1050 #items: array:1 [ 0 => App\Models\Term {#1047 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:7 [ "id" => 29 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Глава" "field_cases" => array:6 [ …6] "field_page_check_not_needed" => null "field_short_name" => null ] #original: array:7 [ "id" => 29 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Глава" "field_cases" => array:6 [ …6] "field_page_check_not_needed" => null "field_short_name" => 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_page_start" => "3" "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 {#1087 #items: array:1 [ 0 => App\Models\Book {#1049 #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" => 80 "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 {#1051 #items: array:1 [ 0 => App\Models\Term {#1048 #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 {#1052 #items: array:1 [ 0 => App\Models\Term {#1053 #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" => 5457 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "8" "field_cases" => array:6 [ …6] "field_translit" => "vosmoj" ] #original: array:6 [ "id" => 5457 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "8" "field_cases" => array:6 [ …6] "field_translit" => "vosmoj" ] #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 {#1054 #items: array:1 [ 0 => App\Models\Term {#1055 #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" => 5153 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Просвещение" "field_cases" => null "field_translit" => "prosveschenie" ] #original: array:6 [ "id" => 5153 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Просвещение" "field_cases" => null "field_translit" => "prosveschenie" ] #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 {#1056 #items: array:6 [ 0 => App\Models\Term {#1057 #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" => 4283 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Дорофеев" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Георгий" "field_patronymic" => "Владимирович" "field_surname_rp" => null ] #original: array:12 [ "id" => 4283 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Дорофеев" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Георгий" "field_patronymic" => "Владимирович" "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 {#1058 #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" => 5879 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Суворова" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Светлана" "field_patronymic" => "Борисовна" "field_surname_rp" => null ] #original: array:12 [ "id" => 5879 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Суворова" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Светлана" "field_patronymic" => "Борисовна" "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 {#1059 #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" => 3941 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Бунимович" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Евгений" "field_patronymic" => "Абрамович" "field_surname_rp" => null ] #original: array:12 [ "id" => 3941 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Бунимович" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Евгений" "field_patronymic" => "Абрамович" "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 => "*" ] } 3 => App\Models\Term {#1060 #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" => 4848 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Кузнецова" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Людмила" "field_patronymic" => "Викторовна" "field_surname_rp" => null ] #original: array:12 [ "id" => 4848 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Кузнецова" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Людмила" "field_patronymic" => "Викторовна" "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 => "*" ] } 4 => App\Models\Term {#1061 #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" => 5198 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Минаева" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Светлана" "field_patronymic" => "Станиславовна" "field_surname_rp" => null ] #original: array:12 [ "id" => 5198 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Минаева" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Светлана" "field_patronymic" => "Станиславовна" "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 => "*" ] } 5 => App\Models\Term {#1062 #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" => 5622 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Рослова" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Лариса" "field_patronymic" => "Олеговна" "field_surname_rp" => null ] #original: array:12 [ "id" => 5622 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Рослова" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Лариса" "field_patronymic" => "Олеговна" "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 {#1063 #items: [] #escapeWhenCastingToString: false } "field_book_type" => Illuminate\Database\Eloquent\Collection {#1064 #items: array:1 [ 0 => App\Models\Term {#1065 #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 {#1066 #items: array:1 [ 0 => App\Models\Term {#1067 #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" => 9 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Россия" "field_cases" => array:6 [ …6] "field_translit" => "rossiya" ] #original: array:6 [ "id" => 9 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Россия" "field_cases" => array:6 [ …6] "field_translit" => "rossiya" ] #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 {#1068 #items: array:1 [ 0 => App\Models\Term {#1069 #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" => 15 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Москва" "field_cases" => array:6 [ …6] "field_translit" => "moskva" ] #original: array:6 [ "id" => 15 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Москва" "field_cases" => array:6 [ …6] "field_translit" => "moskva" ] #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 {#1070 #items: [] #escapeWhenCastingToString: false } "field_umk" => Illuminate\Database\Eloquent\Collection {#1071 #items: [] #escapeWhenCastingToString: false } "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1072 #items: [] #escapeWhenCastingToString: false } "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1073 #items: array:1 [ 0 => App\Models\Term {#1074 #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" => 6706 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "ФГОС (старый)" "field_cases" => array:6 [ …6] "field_color" => null "field_end_year" => "2022" "field_start_year" => "2019" "field_translit" => "fgos-old" "field_type" => null ] #original: array:10 [ "id" => 6706 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "ФГОС (старый)" "field_cases" => array:6 [ …6] "field_color" => null "field_end_year" => "2022" "field_start_year" => "2019" "field_translit" => "fgos-old" "field_type" => 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_publication_number" => "7" "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1075 #items: array:1 [ 0 => App\Models\Term {#1076 #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" => 34 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "переработанное" "field_cases" => array:6 [ …6] "field_translit" => "pererabotannoe" ] #original: array:6 [ "id" => 34 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "переработанное" "field_cases" => array:6 [ …6] "field_translit" => "pererabotannoe" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] 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Так, по крайней мере думают подростки. Однако на практике все получается совершенно по-другому. Поэтому как бы сложен не был предмет (например, алгебра), его необходимо как следует изучить. Чтобы процесс восприятия материала проходил легко и без заминок, следует использовать «<strong>ГДЗ по Алгебре 8 класс Учебник Дорофеев, Суворова, Бунимович, Кузнецова, Минаева, Рослова (Просвещение)</strong>». </p> <p> В справочнике нашли отражение следующие темы: <ol> <li>Алгебраическая дробь, ее свойства, действия с ней.</li> <li>Как преобразовать степень?</li> <li>Теорема Пифагора.</li> <li>График зависимости y=√х.</li> <li>Квадратный и кубический корни.</li> <li>Двойные радикалы, и т.д.</li> </ol> <p> В восьмом классе по предмету проходят спаренные уроки, что с одной стороны должно помочь учителю более подробно объяснить каждую тему. Но на деле и этого времени все равно не хватает, так как программа стала еще обширнее. 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Так как самостоятельно подростки такого мониторинга не проводят, то им поможет в этом <strong>сборник ответов по алгебре 8 класс к учебнику Дорофеева</strong>. </p> <p> Благодаря изданию учащиеся смогут: <ol> <li>улучшить качество письменных работ;</li> <li>избавиться от любых недочетов;</li> <li>приобрести хорошую успеваемость;</li> <li>устранять трудности по мере их возникновения.</li> </ol> <p> Систематически занимаясь с решебником, восьмиклассники научатся не только разбираться в самых непростых темах, но и будут активно применять свои навыки на практике. Это позволит им выбиться в отличники и успешно справляться со всеми поставленными учителем задачами. Кроме того, они могут не переживать о результатах многочисленных проверочных работ, так как будут знать весь материал «на зубок». </p> <h2> Как часто можно использовать онлайн-справочник? </h2> <p> В скором времени учащимся предстоит сдавать первые экзамены, после чего многие из них навсегда покинут школьные стены. Из-за этого на первое место встают успеваемость и качество полученных знаний. Родители стараются всячески помочь детям преодолеть все трудности и нередко записывают их к репетитору. Но намного действеннее могут оказаться занятия с <strong>гдз по алгебре за 8 класс Учебник Дорофеев</strong>. </p> <p> Сборник позволит ученикам: <ul> <li>самостоятельно разобрать все проблемные моменты;</li> <li>дополнительно потренироваться перед контрольными;</li> <li>работать в удобном для себя темпе;</li> <li>не зависеть от помощи взрослых.</li> </ul> <p> Опытные методисты, которые составили решебник, предоставили много полезной информации, благодаря чему никакие дополнительные действия для освоения дисциплины не понадобятся. Но, конечно, если подростки хотят добиться хороших результатов, им стоит забыть о списывании. Необходимо тщательно изучать все сведения, проводить анализ задач и уравнений, чтобы понять принцип их выполнения. Освоив это, восьмиклассники не будут испытывать затруднений при переходе к более сложному материалу. </p>" "breadcrumbs" => array:3 [ "class" => 379 "subject" => 542 "class_subject" => 385 ] ] #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 {#1085 #items: [] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 208891 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Алгебраические дроби" "field_branch_order" => "1" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1050} "field_page_start" => "3" "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 {#1087} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1085} ] #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 {#1123 #items: array:2 [ 0 => App\Models\Branch {#1131 #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" => 208891 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Алгебраические дроби" "field_branch_order" => "1" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1132 #items: array:1 [ 0 => App\Models\Term {#1047} ] #escapeWhenCastingToString: false } "field_page_start" => "3" "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 {#1133 #items: array:1 [ 0 => App\Models\Book {#1049} ] #escapeWhenCastingToString: false } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1134 #items: [] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 208891 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Алгебраические дроби" "field_branch_order" => "1" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1132} "field_page_start" => "3" "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 {#1133} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1134} ] #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 {#1135 #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" => 208896 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "1.5. Преобразование выражений, содержащих алгебраические дроби" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1136 #items: [] #escapeWhenCastingToString: false } "field_page_start" => "28" "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 {#1137 #items: array:1 [ 0 => App\Models\Book {#1049} ] #escapeWhenCastingToString: false } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1138 #items: array:1 [ 0 => App\Models\Branch {#1045} ] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 208896 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "1.5. Преобразование выражений, содержащих алгебраические дроби" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1136} "field_page_start" => "28" "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 {#1137} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1138} ] #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 {#1120 #items: array:5 [ 0 => App\Models\Element {#1110 #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" => 233004 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1101 #items: array:1 [ 0 => App\Models\Edition {#1111 #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" => 729 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Условие" "field_order" => "1" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1109 …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" => "tolik" "field_edition_type" => "statement" "field_root_dir" => "0-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1107 …2} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1106 …2} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1105 …2} "field_content_source" => null ] #original: array:21 [ "id" => 729 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Условие" "field_order" => "1" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1109 …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" => "tolik" "field_edition_type" => "statement" "field_root_dir" => "0-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1107 …2} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1106 …2} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1105 …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" => "209102" "type" => "task" ] "text" => "<p><strong>93 a)</strong> $ \frac{a}{1-b} + \frac{a^2-ab}{b^2-1} \cdot \frac{b+1}{a} $</p><p><strong>б)</strong> $ \frac{m^2-9}{m} : \frac{(m-3)^2}{m} + \frac{6}{3-m} $</p><p><strong>В)</strong> $ n - \frac{n^2-na}{n+a} \cdot \frac{n}{n-a} $</p><p><strong>Г)</strong> $ \frac{v+3}{1-v} + \frac{v+3}{v-1} \cdot (v+1) $</p>" "img" => array:1 [ 0 => array:5 [ "name" => "93-1.jpg" "alt" => null "width" => "1401" "height" => 310 "path" => "/media/algebra_08/dorofeev/0-00/93-1.webp?ts=1734264146" ] ] ] #original: array:7 [ "id" => 233004 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1101} "task" => array:2 [ "refs" => "209102" "type" => "task" ] "text" => "<p><strong>93 a)</strong> $ \frac{a}{1-b} + \frac{a^2-ab}{b^2-1} \cdot \frac{b+1}{a} $</p><p><strong>б)</strong> $ \frac{m^2-9}{m} : \frac{(m-3)^2}{m} + \frac{6}{3-m} $</p><p><strong>В)</strong> $ n - \frac{n^2-na}{n+a} \cdot \frac{n}{n-a} $</p><p><strong>Г)</strong> $ \frac{v+3}{1-v} + \frac{v+3}{v-1} \cdot (v+1) $</p>" "img" => array:1 [ 0 => array:5 [ "name" => "93-1.jpg" "alt" => null "width" => "1401" "height" => 310 "path" => "/media/algebra_08/dorofeev/0-00/93-1.webp?ts=1734264146" ] ] ] #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 {#1103 #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" => 234210 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1095 #items: array:1 [ 0 => App\Models\Edition {#1104 #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" => 730 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Решение 1" "field_order" => "2" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1099 …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" => "tolik" "field_edition_type" => "solution" "field_root_dir" => "1-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1100 …2} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1098 …2} "field_process_formula" => "" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1091 …2} "field_content_source" => null ] #original: array:21 [ "id" => 730 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Решение 1" "field_order" => "2" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1099 …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" => "tolik" "field_edition_type" => "solution" "field_root_dir" => "1-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1100 …2} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1098 …2} "field_process_formula" => "" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1091 …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" => "209102" "type" => "task" ] "img" => array:4 [ 0 => array:5 [ "name" => "93-1.png" "alt" => null "width" => "705" "height" => 1748 "path" => "/media/algebra_08/dorofeev/1-00/93-1.webp?ts=1734264997" ] 1 => array:5 [ "name" => "93-2.png" "alt" => null "width" => "705" "height" => 1909 "path" => "/media/algebra_08/dorofeev/1-00/93-2.webp?ts=1734264997" ] 2 => array:5 [ "name" => "93-3.png" "alt" => null "width" => "705" "height" => 1476 "path" => "/media/algebra_08/dorofeev/1-00/93-3.webp?ts=1734264997" ] 3 => array:5 [ "name" => "93-4.png" "alt" => null "width" => "705" "height" => 1619 "path" => "/media/algebra_08/dorofeev/1-00/93-4.webp?ts=1734264997" ] ] ] #original: array:6 [ "id" => 234210 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1095} "task" => array:2 [ "refs" => "209102" "type" => "task" ] "img" => array:4 [ 0 => array:5 [ "name" => "93-1.png" "alt" => null "width" => "705" "height" => 1748 "path" => "/media/algebra_08/dorofeev/1-00/93-1.webp?ts=1734264997" ] 1 => array:5 [ "name" => "93-2.png" "alt" => null "width" => "705" "height" => 1909 "path" => "/media/algebra_08/dorofeev/1-00/93-2.webp?ts=1734264997" ] 2 => array:5 [ "name" => "93-3.png" "alt" => null "width" => "705" "height" => 1476 "path" => "/media/algebra_08/dorofeev/1-00/93-3.webp?ts=1734264997" ] 3 => array:5 [ "name" => "93-4.png" "alt" => null "width" => "705" "height" => 1619 "path" => "/media/algebra_08/dorofeev/1-00/93-4.webp?ts=1734264997" ] ] ] #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 {#1097 #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" => 234376 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1043 #items: array:1 [ 0 => App\Models\Edition {#1096 #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" => 731 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Решение 2" "field_order" => "3" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1093 …2} "field_content_type" => "free" "field_content_mode" => "image" 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"task" ] "text" => "<p><strong>а)</strong> $ \frac{a}{1-b} + \frac{a^2-ab}{b^2-1} \cdot \frac{b+1}{a} $</p><p>1. Сначала выполним умножение. Для этого разложим числитель первой дроби и знаменатель на множители. В числителе вынесем общий множитель $a$ за скобки, а в знаменателе используем формулу разности квадратов $x^2-y^2=(x-y)(x+y)$.</p><p>$ \frac{a^2-ab}{b^2-1} \cdot \frac{b+1}{a} = \frac{a(a-b)}{(b-1)(b+1)} \cdot \frac{b+1}{a} $</p><p>2. Сократим одинаковые множители в числителе и знаменателе ($a$ и $b+1$):</p><p>$ \frac{\cancel{a}(a-b)}{(b-1)(\cancel{b+1})} \cdot \frac{\cancel{b+1}}{\cancel{a}} = \frac{a-b}{b-1} $</p><p>3. Теперь выполним сложение с первой дробью. Исходное выражение принимает вид:</p><p>$ \frac{a}{1-b} + \frac{a-b}{b-1} $</p><p>4. Чтобы привести дроби к общему знаменателю, заметим, что $1-b = -(b-1)$. Вынесем минус из знаменателя первой дроби:</p><p>$ \frac{a}{-(b-1)} + \frac{a-b}{b-1} = -\frac{a}{b-1} + \frac{a-b}{b-1} $</p><p>5. Теперь, когда знаменатели одинаковы, сложим числители:</p><p>$ \frac{-a + (a-b)}{b-1} = \frac{-a+a-b}{b-1} = \frac{-b}{b-1} $</p><p>Выражение также можно записать в виде $ \frac{b}{1-b} $.</p><p>Ответ: $ \frac{-b}{b-1} $</p><p><strong>б)</strong> $ \frac{m^2-9}{m} : \frac{(m-3)^2}{m} + \frac{6}{3-m} $</p><p>1. Согласно порядку действий, сначала выполним деление. Деление на дробь равносильно умножению на обратную ей дробь:</p><p>$ \frac{m^2-9}{m} : \frac{(m-3)^2}{m} = \frac{m^2-9}{m} \cdot \frac{m}{(m-3)^2} $</p><p>2. Разложим числитель $ m^2-9 $ по формуле разности квадратов:</p><p>$ \frac{(m-3)(m+3)}{m} \cdot \frac{m}{(m-3)^2} $</p><p>3. Сократим общие множители $m$ и $(m-3)$:</p><p>$ \frac{(\cancel{m-3})(m+3)}{\cancel{m}} \cdot \frac{\cancel{m}}{(m-3)^{\cancel{2}}} = \frac{m+3}{m-3} $</p><p>4. Теперь выполним сложение:</p><p>$ \frac{m+3}{m-3} + \frac{6}{3-m} $</p><p>5. Приведем дроби к общему знаменателю. Заметим, что $3-m = -(m-3)$.</p><p>$ \frac{m+3}{m-3} + \frac{6}{-(m-3)} = \frac{m+3}{m-3} - \frac{6}{m-3} $</p><p>6. Выполним вычитание числителей:</p><p>$ \frac{(m+3)-6}{m-3} = \frac{m-3}{m-3} = 1 $</p><p>При этом $ m \ne 0 $ и $ m \ne 3 $.</p><p>Ответ: $1$</p><p><strong>в)</strong> $ n - \frac{n^2-na}{n+a} \cdot \frac{n}{n-a} $</p><p>1. Сначала выполним умножение дробей. В числителе первой дроби вынесем $n$ за скобки:</p><p>$ \frac{n^2-na}{n+a} \cdot \frac{n}{n-a} = \frac{n(n-a)}{n+a} \cdot \frac{n}{n-a} $</p><p>2. Сократим общий множитель $(n-a)$:</p><p>$ \frac{n(\cancel{n-a})}{n+a} \cdot \frac{n}{\cancel{n-a}} = \frac{n \cdot n}{n+a} = \frac{n^2}{n+a} $</p><p>3. Теперь выполним вычитание:</p><p>$ n - \frac{n^2}{n+a} $</p><p>4. Приведем $n$ к общему знаменателю $(n+a)$:</p><p>$ \frac{n(n+a)}{n+a} - \frac{n^2}{n+a} = \frac{n^2+na}{n+a} - \frac{n^2}{n+a} $</p><p>5. Выполним вычитание числителей:</p><p>$ \frac{(n^2+na) - n^2}{n+a} = \frac{n^2+na-n^2}{n+a} = \frac{na}{n+a} $</p><p>Ответ: $ \frac{na}{n+a} $</p><p><strong>г)</strong> $ \frac{v+3}{1-v} + \frac{v+3}{v-1} \cdot (v+1) $</p><p>1. По порядку действий сначала выполняем умножение:</p><p>$ \frac{v+3}{v-1} \cdot (v+1) = \frac{(v+3)(v+1)}{v-1} = \frac{v^2+v+3v+3}{v-1} = \frac{v^2+4v+3}{v-1} $</p><p>2. Теперь выполним сложение:</p><p>$ \frac{v+3}{1-v} + \frac{v^2+4v+3}{v-1} $</p><p>3. Приведем дроби к общему знаменателю, используя $1-v = -(v-1)$:</p><p>$ \frac{v+3}{-(v-1)} + \frac{v^2+4v+3}{v-1} = -\frac{v+3}{v-1} + \frac{v^2+4v+3}{v-1} $</p><p>4. Сложим числители:</p><p>$ \frac{-(v+3) + (v^2+4v+3)}{v-1} = \frac{-v-3+v^2+4v+3}{v-1} $</p><p>5. Упростим числитель:</p><p>$ \frac{v^2 + (-v+4v) + (-3+3)}{v-1} = \frac{v^2+3v}{v-1} $</p><p>6. Можно вынести общий множитель $v$ в числителе:</p><p>$ \frac{v(v+3)}{v-1} $</p><p>Ответ: $ \frac{v(v+3)}{v-1} $</p>" ] #original: array:6 [ "id" => 1373261 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1144} "task" => array:2 [ "refs" => "209102" "type" => "task" ] "text" => "<p><strong>а)</strong> $ \frac{a}{1-b} + \frac{a^2-ab}{b^2-1} \cdot \frac{b+1}{a} $</p><p>1. Сначала выполним умножение. Для этого разложим числитель первой дроби и знаменатель на множители. В числителе вынесем общий множитель $a$ за скобки, а в знаменателе используем формулу разности квадратов $x^2-y^2=(x-y)(x+y)$.</p><p>$ \frac{a^2-ab}{b^2-1} \cdot \frac{b+1}{a} = \frac{a(a-b)}{(b-1)(b+1)} \cdot \frac{b+1}{a} $</p><p>2. Сократим одинаковые множители в числителе и знаменателе ($a$ и $b+1$):</p><p>$ \frac{\cancel{a}(a-b)}{(b-1)(\cancel{b+1})} \cdot \frac{\cancel{b+1}}{\cancel{a}} = \frac{a-b}{b-1} $</p><p>3. Теперь выполним сложение с первой дробью. Исходное выражение принимает вид:</p><p>$ \frac{a}{1-b} + \frac{a-b}{b-1} $</p><p>4. Чтобы привести дроби к общему знаменателю, заметим, что $1-b = -(b-1)$. Вынесем минус из знаменателя первой дроби:</p><p>$ \frac{a}{-(b-1)} + \frac{a-b}{b-1} = -\frac{a}{b-1} + \frac{a-b}{b-1} $</p><p>5. Теперь, когда знаменатели одинаковы, сложим числители:</p><p>$ \frac{-a + (a-b)}{b-1} = \frac{-a+a-b}{b-1} = \frac{-b}{b-1} $</p><p>Выражение также можно записать в виде $ \frac{b}{1-b} $.</p><p>Ответ: $ \frac{-b}{b-1} $</p><p><strong>б)</strong> $ \frac{m^2-9}{m} : \frac{(m-3)^2}{m} + \frac{6}{3-m} $</p><p>1. Согласно порядку действий, сначала выполним деление. Деление на дробь равносильно умножению на обратную ей дробь:</p><p>$ \frac{m^2-9}{m} : \frac{(m-3)^2}{m} = \frac{m^2-9}{m} \cdot \frac{m}{(m-3)^2} $</p><p>2. Разложим числитель $ m^2-9 $ по формуле разности квадратов:</p><p>$ \frac{(m-3)(m+3)}{m} \cdot \frac{m}{(m-3)^2} $</p><p>3. Сократим общие множители $m$ и $(m-3)$:</p><p>$ \frac{(\cancel{m-3})(m+3)}{\cancel{m}} \cdot \frac{\cancel{m}}{(m-3)^{\cancel{2}}} = \frac{m+3}{m-3} $</p><p>4. Теперь выполним сложение:</p><p>$ \frac{m+3}{m-3} + \frac{6}{3-m} $</p><p>5. Приведем дроби к общему знаменателю. Заметим, что $3-m = -(m-3)$.</p><p>$ \frac{m+3}{m-3} + \frac{6}{-(m-3)} = \frac{m+3}{m-3} - \frac{6}{m-3} $</p><p>6. Выполним вычитание числителей:</p><p>$ \frac{(m+3)-6}{m-3} = \frac{m-3}{m-3} = 1 $</p><p>При этом $ m \ne 0 $ и $ m \ne 3 $.</p><p>Ответ: $1$</p><p><strong>в)</strong> $ n - \frac{n^2-na}{n+a} \cdot \frac{n}{n-a} $</p><p>1. Сначала выполним умножение дробей. В числителе первой дроби вынесем $n$ за скобки:</p><p>$ \frac{n^2-na}{n+a} \cdot \frac{n}{n-a} = \frac{n(n-a)}{n+a} \cdot \frac{n}{n-a} $</p><p>2. Сократим общий множитель $(n-a)$:</p><p>$ \frac{n(\cancel{n-a})}{n+a} \cdot \frac{n}{\cancel{n-a}} = \frac{n \cdot n}{n+a} = \frac{n^2}{n+a} $</p><p>3. Теперь выполним вычитание:</p><p>$ n - \frac{n^2}{n+a} $</p><p>4. Приведем $n$ к общему знаменателю $(n+a)$:</p><p>$ \frac{n(n+a)}{n+a} - \frac{n^2}{n+a} = \frac{n^2+na}{n+a} - \frac{n^2}{n+a} $</p><p>5. Выполним вычитание числителей:</p><p>$ \frac{(n^2+na) - n^2}{n+a} = \frac{n^2+na-n^2}{n+a} = \frac{na}{n+a} $</p><p>Ответ: $ \frac{na}{n+a} $</p><p><strong>г)</strong> $ \frac{v+3}{1-v} + \frac{v+3}{v-1} \cdot (v+1) $</p><p>1. По порядку действий сначала выполняем умножение:</p><p>$ \frac{v+3}{v-1} \cdot (v+1) = \frac{(v+3)(v+1)}{v-1} = \frac{v^2+v+3v+3}{v-1} = \frac{v^2+4v+3}{v-1} $</p><p>2. Теперь выполним сложение:</p><p>$ \frac{v+3}{1-v} + \frac{v^2+4v+3}{v-1} $</p><p>3. Приведем дроби к общему знаменателю, используя $1-v = -(v-1)$:</p><p>$ \frac{v+3}{-(v-1)} + \frac{v^2+4v+3}{v-1} = -\frac{v+3}{v-1} + \frac{v^2+4v+3}{v-1} $</p><p>4. Сложим числители:</p><p>$ \frac{-(v+3) + (v^2+4v+3)}{v-1} = \frac{-v-3+v^2+4v+3}{v-1} $</p><p>5. Упростим числитель:</p><p>$ \frac{v^2 + (-v+4v) + (-3+3)}{v-1} = \frac{v^2+3v}{v-1} $</p><p>6. Можно вынести общий множитель $v$ в числителе:</p><p>$ \frac{v(v+3)}{v-1} $</p><p>Ответ: $ \frac{v(v+3)}{v-1} $</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" => "209103" "type" => "task" ] "previous" => array:2 [ "refs" => "209101" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1113 #items: array:1 [ 0 => App\Models\Book {#1049} ] #escapeWhenCastingToString: false } "page" => Illuminate\Database\Eloquent\Collection {#1116 #items: array:1 [ 0 => App\Models\BookPage {#1115 #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" => 929801 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "30" "field_url" => "/8-klass/algebra/dorofeev-uchebnik/page-30" "field_display_title" => "30" "field_folder" => "1" "field_image_name" => "30" "field_branch_parent" => Illuminate\Database\Eloquent\Collection {#1042 #items: [] #escapeWhenCastingToString: false } "field_weight" => "0" "field_book_parent" => Illuminate\Database\Eloquent\Collection {#1119 #items: array:1 [ 0 => App\Models\Book {#1049} ] #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 {#1040 #items: [] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1152 #items: array:1 [ 0 => App\Models\Element {#1151 #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" => 1104324 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1153 …2} "book_page" => array:2 [ …2] "img" => array:1 [ …1] ] #original: array:6 [ "id" => 1104324 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1153 …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" => "929802" "type" => "book_page" ] "previous" => array:2 [ "refs" => "929800" "type" => "book_page" ] "tasks" => Illuminate\Database\Eloquent\Collection {#1246 #items: array:6 [ 0 => App\Models\Task {#1258 #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" => 209100 …23 ] #original: array:24 [ …24] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } 1 => App\Models\Task {#1264 #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 [ …24] #original: array:24 [ …24] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } 2 => App\Models\Task {#1268 #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 [ …24] #original: array:24 [ …24] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } 3 => App\Models\Task {#1269 #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 [ …24] #original: array:24 [ …24] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } 4 => App\Models\Task {#1307 #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 [ …24] #original: array:24 [ …24] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } 5 => App\Models\Task {#1311 #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 [ …24] #original: array:24 [ …24] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } ] #escapeWhenCastingToString: false } ] #original: array:21 [ "id" => 929801 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "30" "field_url" => "/8-klass/algebra/dorofeev-uchebnik/page-30" "field_display_title" => "30" "field_folder" => "1" 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"929801" "type" => "book_page" ] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] }
№93 (с. 30)
Условие. №93 (с. 30)
скриншот условия
93 a) $ \frac{a}{1-b} + \frac{a^2-ab}{b^2-1} \cdot \frac{b+1}{a} $
б) $ \frac{m^2-9}{m} : \frac{(m-3)^2}{m} + \frac{6}{3-m} $
В) $ n - \frac{n^2-na}{n+a} \cdot \frac{n}{n-a} $
Г) $ \frac{v+3}{1-v} + \frac{v+3}{v-1} \cdot (v+1) $
Решение 1. №93 (с. 30)
Решение 2. №93 (с. 30)
Решение 3. №93 (с. 30)
Решение 4. №93 (с. 30)
а) $ \frac{a}{1-b} + \frac{a^2-ab}{b^2-1} \cdot \frac{b+1}{a} $
1. Сначала выполним умножение. Для этого разложим числитель первой дроби и знаменатель на множители. В числителе вынесем общий множитель $a$ за скобки, а в знаменателе используем формулу разности квадратов $x^2-y^2=(x-y)(x+y)$.
$ \frac{a^2-ab}{b^2-1} \cdot \frac{b+1}{a} = \frac{a(a-b)}{(b-1)(b+1)} \cdot \frac{b+1}{a} $
2. Сократим одинаковые множители в числителе и знаменателе ($a$ и $b+1$):
$ \frac{\cancel{a}(a-b)}{(b-1)(\cancel{b+1})} \cdot \frac{\cancel{b+1}}{\cancel{a}} = \frac{a-b}{b-1} $
3. Теперь выполним сложение с первой дробью. Исходное выражение принимает вид:
$ \frac{a}{1-b} + \frac{a-b}{b-1} $
4. Чтобы привести дроби к общему знаменателю, заметим, что $1-b = -(b-1)$. Вынесем минус из знаменателя первой дроби:
$ \frac{a}{-(b-1)} + \frac{a-b}{b-1} = -\frac{a}{b-1} + \frac{a-b}{b-1} $
5. Теперь, когда знаменатели одинаковы, сложим числители:
$ \frac{-a + (a-b)}{b-1} = \frac{-a+a-b}{b-1} = \frac{-b}{b-1} $
Выражение также можно записать в виде $ \frac{b}{1-b} $.
Ответ: $ \frac{-b}{b-1} $
б) $ \frac{m^2-9}{m} : \frac{(m-3)^2}{m} + \frac{6}{3-m} $
1. Согласно порядку действий, сначала выполним деление. Деление на дробь равносильно умножению на обратную ей дробь:
$ \frac{m^2-9}{m} : \frac{(m-3)^2}{m} = \frac{m^2-9}{m} \cdot \frac{m}{(m-3)^2} $
2. Разложим числитель $ m^2-9 $ по формуле разности квадратов:
$ \frac{(m-3)(m+3)}{m} \cdot \frac{m}{(m-3)^2} $
3. Сократим общие множители $m$ и $(m-3)$:
$ \frac{(\cancel{m-3})(m+3)}{\cancel{m}} \cdot \frac{\cancel{m}}{(m-3)^{\cancel{2}}} = \frac{m+3}{m-3} $
4. Теперь выполним сложение:
$ \frac{m+3}{m-3} + \frac{6}{3-m} $
5. Приведем дроби к общему знаменателю. Заметим, что $3-m = -(m-3)$.
$ \frac{m+3}{m-3} + \frac{6}{-(m-3)} = \frac{m+3}{m-3} - \frac{6}{m-3} $
6. Выполним вычитание числителей:
$ \frac{(m+3)-6}{m-3} = \frac{m-3}{m-3} = 1 $
При этом $ m \ne 0 $ и $ m \ne 3 $.
Ответ: $1$
в) $ n - \frac{n^2-na}{n+a} \cdot \frac{n}{n-a} $
1. Сначала выполним умножение дробей. В числителе первой дроби вынесем $n$ за скобки:
$ \frac{n^2-na}{n+a} \cdot \frac{n}{n-a} = \frac{n(n-a)}{n+a} \cdot \frac{n}{n-a} $
2. Сократим общий множитель $(n-a)$:
$ \frac{n(\cancel{n-a})}{n+a} \cdot \frac{n}{\cancel{n-a}} = \frac{n \cdot n}{n+a} = \frac{n^2}{n+a} $
3. Теперь выполним вычитание:
$ n - \frac{n^2}{n+a} $
4. Приведем $n$ к общему знаменателю $(n+a)$:
$ \frac{n(n+a)}{n+a} - \frac{n^2}{n+a} = \frac{n^2+na}{n+a} - \frac{n^2}{n+a} $
5. Выполним вычитание числителей:
$ \frac{(n^2+na) - n^2}{n+a} = \frac{n^2+na-n^2}{n+a} = \frac{na}{n+a} $
Ответ: $ \frac{na}{n+a} $
г) $ \frac{v+3}{1-v} + \frac{v+3}{v-1} \cdot (v+1) $
1. По порядку действий сначала выполняем умножение:
$ \frac{v+3}{v-1} \cdot (v+1) = \frac{(v+3)(v+1)}{v-1} = \frac{v^2+v+3v+3}{v-1} = \frac{v^2+4v+3}{v-1} $
2. Теперь выполним сложение:
$ \frac{v+3}{1-v} + \frac{v^2+4v+3}{v-1} $
3. Приведем дроби к общему знаменателю, используя $1-v = -(v-1)$:
$ \frac{v+3}{-(v-1)} + \frac{v^2+4v+3}{v-1} = -\frac{v+3}{v-1} + \frac{v^2+4v+3}{v-1} $
4. Сложим числители:
$ \frac{-(v+3) + (v^2+4v+3)}{v-1} = \frac{-v-3+v^2+4v+3}{v-1} $
5. Упростим числитель:
$ \frac{v^2 + (-v+4v) + (-3+3)}{v-1} = \frac{v^2+3v}{v-1} $
6. Можно вынести общий множитель $v$ в числителе:
$ \frac{v(v+3)}{v-1} $
Ответ: $ \frac{v(v+3)}{v-1} $
Другие задания:
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