Basic algebra problem: $\frac{\frac{1}{x}+\frac{1}{y}}{\frac{1}{{x}^{2}}-\frac{1}{{y}^{2}}}$

$x,y\in \mathbb{R},{x}^{2}\ne {y}^{2},xy\ne 0$

Now I know the result is: $\frac{xy}{y-x}$, but I am not sure how to get it, I get into a mess like this: $=x+\frac{{x}^{2}}{y}-\frac{{y}^{2}}{x}-y=\frac{x(xy)+{x}^{3}-{y}^{3}-y(xy)}{xy}=?$ which doesn't seem to help me much. Halp please.

$x,y\in \mathbb{R},{x}^{2}\ne {y}^{2},xy\ne 0$

Now I know the result is: $\frac{xy}{y-x}$, but I am not sure how to get it, I get into a mess like this: $=x+\frac{{x}^{2}}{y}-\frac{{y}^{2}}{x}-y=\frac{x(xy)+{x}^{3}-{y}^{3}-y(xy)}{xy}=?$ which doesn't seem to help me much. Halp please.