Question

Упростите выражение:

Answer 1

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