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iliyar2001
@iliyar2001
July 2022
1
6
Report
Выполните указанные действия:
1 3ab b-a
------ - ----------- - ------------
a-b a^3-b^3 a^2+ab+b^2
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Answers & Comments
Marzha777
Общий знаменатель a³-b³=(a-b)(a²+ab+b²)
получаем числитель (a²+ab+b²)-3ab-(b-a)(a-b)=
=a²+ab+b²-3ab+(a-b)(a-b)=a²+ab+b²-3ab+(a-b)²=
=
a²
+
ab
+b²
-
3ab
+
a²
-
2ab
+b²=2a²+-4ab 2b²=2(a²-2ab+b²)=2(a-b)²
Подставляем в дробь
2(a-b)²
(a-b)(a²+ab+b²)
2(a-b)
(a²+ab+b²)
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Answers & Comments
получаем числитель (a²+ab+b²)-3ab-(b-a)(a-b)=
=a²+ab+b²-3ab+(a-b)(a-b)=a²+ab+b²-3ab+(a-b)²=
=a²+ab+b²-3ab+a²-2ab+b²=2a²+-4ab 2b²=2(a²-2ab+b²)=2(a-b)²
Подставляем в дробь
2(a-b)²
(a-b)(a²+ab+b²)
2(a-b)
(a²+ab+b²)