Question

Выполните действие! 1) (2х-y\2x+y-2x+y\2x-y):4xy\y^2-4x^2)

Answer 1

$( \frac{2x-y}{2x+y}- \frac{2x+y}{2x-y}): \frac{4xy}{y^2-4x^2} = \frac{(2x-y)(2x-y)-(2x+y)(2x+y)}{(2x+y)(2x-y)}* \frac{y^2-4x^2}{4xy}=$$-\frac{(2x-y)^2-(2x+y)^2}{(2x+y)(2x-y)}* \frac{4x^2-y^2}{4xy}=$$-\frac{((2x-y)+(2x+y))((2x-y)-(2x+y))}{(2x+y)(2x-y)}* \frac{(2x-y)(2x+y)}{4xy}=$$-\frac{(2x-y+2x+y)(2x-y-2x-y))}{1}* \frac{1}{4xy}=-\frac{4x*(-2y)}{1}* \frac{1}{4xy}=\frac{8xy}{4xy}=2$