Answer
$-\frac{x^2+y^2}{(x-y)^2}$
Work Step by Step
Multiply $\frac{x^2y^2}{x^2y^2}$ to the expression, we have:
$\frac{x^{-2}+y^{-2}}{x^{-2}-y^{-2}}\cdot \frac{x+y}{x-y}=\frac{x^2y^2}{x^2y^2}\cdot\frac{x^{-2}+y^{-2}}{x^{-2}-y^{-2}}\cdot \frac{x+y}{x-y}=\frac{y^2+x^2}{y^2-x^2}\cdot \frac{x+y}{x-y}=\frac{x^2+y^2}{(y+x)(y-x)}\cdot \frac{x+y}{x-y}=-\frac{x^2+y^2}{(x-y)^2}$
