Question

Упростите выражение:

Answer 1

$= (frac{2x}{2x+y} - frac{4x^2}{(2x+y)^2} ):( frac{2x}{(2x-y)(2x+y)} - frac{1}{2x-y} )= \ \ =frac{2x(2x+y)-4x^2}{(2x+y)^2} : frac{2x-(2x+y)}{(2x-y)(2x+y)} = frac{4x^2+2xy-4x^2}{(2x+y)^2} : frac{2x-2x-y}{(2x-y)(2x+y)} = \ \ = frac{2xy}{(2x+y)^2} : frac{-y}{(2x-y)(2x+y)} = frac{2xy}{(2x+y)^2} * frac{(2x-y)(2x+y)}{-y} = \ \ =frac{-2x(2x-y)}{2x+y} = frac{2xy-4x^2}{2x+y}$