\(\left(\dfrac{2x}{2x+y}-\dfrac{4x^2}{4x^2+4xy+y^2}\right):\left(\dfrac{2x}{4x^2-y^2}+\dfrac{1}{y-2x}\right)\)
=\(\left[\dfrac{2x}{2x+y}-\dfrac{4x^2}{\left(2x+y\right)^2}\right]:\left[\dfrac{2x}{\left(2x-y\right)\left(2x+y\right)}-\dfrac{1}{2x-y}\right]\)
\(=\left[\dfrac{2x\left(2x+y\right)}{\left(2x+y\right)^2}-\dfrac{4x^2}{\left(2x+y\right)^2}\right]:\left[\dfrac{2x}{\left(2x-y\right)\left(2x+y\right)}-\dfrac{y+2x}{\left(2x-y\right)\left(y+2x\right)}\right]\)
\(=\left[\dfrac{4x^2+2xy-4x^2}{\left(2x+y\right)^2}\right]:[\dfrac{2x-y-2x}{\left(2x-y\right)\left(2x+y\right)}]\)
\(=\dfrac{2xy}{\left(2x+y\right)^2}:\dfrac{-y}{\left(2x-y\right)\left(2x+y\right)}\)
\(=\dfrac{2xy\left(2x-y\right)\left(2x+y\right)}{\left(2x+y\right)\left(2x+y\right)\left(-y\right)}\)
\(=\dfrac{2x\left(2x-y\right)}{-\left(2x+y\right)}\)
\(\dfrac{4x^2-2xy}{-2x-y}\)
