Question

Упростите выражение:
$\frac{4y}{y ^{2}- x^{2} } - \frac{2}{y-x}$

Answer 1

$\frac{4y}{y^2-x^2}- \frac{2}{y-x}= \frac{4y}{(y-x)(y+x)}-\frac{2}{y-x}= \frac{4y-2(y+x)}{(y-x)(y+x)}=\frac{4y-2y-2x}{(y-x)(y+x)}=\\=\frac{2y-2x}{(y-x)(y+x)}=\frac{2(y-x)}{(y-x)(y+x)}=\frac{2}{y+x}$