Question

Упростите неравенство.
$\frac{a}{a+b} - \frac{b}{b-a} - \frac{2ab}{ a^{2}- b^{2}}$

Answer 1

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