Question

довести тотожність/ довести тождество

Answer 1

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

$=>-frac{y}{x+y}+frac{y}{x+y}=0$