Довести тотожність/ довести тождество

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

-\frac{y}{x+y}+\frac{y}{x+y}=0" alt="=>-\frac{y}{x+y}+\frac{y}{x+y}=0" align="absmiddle" class="latex-formula">