Question

Выражение (2ab/a^2-b^2+ a-b/2a+2b)*2a/a+b+ b/b-a

Answer 1

$\dispaystyle (\frac{2ab}{a^2-b^2}+ \frac{a-b}{2(a+b)})* \frac{2a}{a+b}+ \frac{b}{b-a}=\\\\=( \frac{4ab+(a-b)^2}{2(a^2-b^2)})* \frac{2a}{a+b}+ \frac{b}{b-a}=\\\\=( \frac{4ab+a^2-2ab+b^2}{2(a^2-b^2)})* \frac{2a}{a+b}+ \frac{b}{b-a}=\\\\= (\frac{(a+b)^2}{2(a^2-b^2)})* \frac{2a}{a+b}+ \frac{b}{b-a}=\\\\= \frac{a+b}{2(a-b)}* \frac{2a}{a+b}+ \frac{b}{b-a}= \frac{a}{a-b}+ \frac{b}{b-a}= \frac{a-b}{a-b}=1$