Question

Упростите выражение
$( frac{1}{x ^{2}-2xy+y ^{2} }- frac{1}{x ^{2} -y ^{2} } ): frac{2y ^{2} }{xy+x ^{2} }$

Answer 1

$(frac{1}{x^2-2xy+y^2}-frac{1}{x^2-y^2}):frac{2y^2}{xy+x^2}=\ (frac{1}{(x-y)^2}-frac{1}{(x-y)(x+y)}):frac{2y^2}{x(x+y)}=\ (frac{x+y-x+y}{(x-y)(x+y)}):frac{2y^2}{x(x+y)}=\ frac{2y}{(x-y)(x+y)}*frac{x(x+y)}{2y^2}=frac{x}{y(x-y)}$