Question

пожалуйста помогите срочно​

Answer 1

Ответ:

$\frac{-b+a}{ab}$

Объяснение:

$\frac{4b}{a^{2}-b^{2}} + \frac{a-b}{a^{2}+ab} + \frac{a+b}{b^{2}-ab } = \frac{4b}{(a-b)(a+b)}+\frac{a-b}{a(a+b)}+\frac{a+b}{b(b-a} = \frac{4b}{(a-b)(a+b)} + \frac{a-b}{a(a+b)} + \frac{a+b}{b(-(a-b))} = \frac{4b}{(a-b)(a+b)} + \frac{a-b}{a(a+b)} - \frac{a+b}{b(a-b)} = \frac{4ab^{2} +b(a-b)^{2}-a(a+b)^{2} }{ab(a+b)(a-b)} = \frac{4ab^{2} +b(a^{2}-2ab+b^{2})-a(a^{2} +2ab+b^{2})}{ab(a^{2}-b^{2})} =$

$\frac{4ab^{2}+a^{2}b-2ab^{2} +b^{3}-a^{3}-2a^{2}b-ab^{2}}{ab(a-b)(a+b)}= \frac{ab^{2}-a^{2}b+b^{3}-a^{3}}{ab(a-b)(a+b)} =\frac{ab(b-a)+(b-a)(b^{2}+ab+a^{2})}{ab(a-b)(a+b)} = \frac{-(a-b)(2ab+b^{2}+a^{2})}{ab(a-b)(a+b)} = \frac{-(b^{2}+2ab+a^{2})}{ab(a-b)(a+b)} = \frac{-(b+a)^{2}}{ab(a+b)} = \frac{-b+a}{ab}$