Question

((x-2y/x^2+2xy)-(x+2y/x^2-2xy)):(4y^2)/(4y^2-x^2)

Answer 1

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