Упростите выражение: [tex]1.(a-b+ \frac{4ab}{a-b} )*( \frac{4a^{2} }{ a^{2}+2ab+b^{2} } - \frac{2a}{a+b} )[/tex] [/tex]. Created by banana27. algebra-ru

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Упростите выражение:
[tex]1.(a-b+ \frac{4ab}{a-b} )*( \frac{4a^{2} }{ a^{2}+2ab+b^{2} } - \frac{2a}{a+b} )[/tex]

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Answers & Comments

A1dar 1) $a-b+\frac{4ab}{a-b}=\frac{(a-b)^2+4ab}{a-b}=\frac{a^2-2ab+b^2+4ab}{a-b}=\frac{a^2+2ab+b^2}{a-b}=\frac{(a+b)^2}{a-b}$
2) $\frac{4a^2}{a^2+2ab+b^2}-\frac{2a}{a+b}=\frac{4a^2-2a(a+b)}{(a+b)^2}=\frac{4a^2-2a^2-2ab}{(a+b)^2}=\frac{2a^2-2ab}{(a+b)^2}=\frac{2a(a-b)}{(a+b)^2}$
3) $\frac{(a+b)^2}{a-b}*\frac{2a(a-b)}{(a+b)^2}=\frac{2a(a+b)^2(a-b)}{(a-b)(a+b)^2}=2a$
Ответ: 2a

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