Question

Помогите упростить выражение.

Answer 1

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