Basic algebra problem: $ \frac{\frac{1}{x}+\frac{1}{y}}{\frac{1}{x^2}-\frac{1}{y^2}} $ Basic algebra problem I can't seem to figure out: $$ \frac{\frac{1}{x}+\frac{1}{y}}{\frac{1}{x^2}-\frac{1}{y^2}} $$ $x,y \in \mathbb{R}, x^2 \neq y^2, xy\neq0$.
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.

$$\frac { \frac { 1 }{ x } +\frac { 1 }{ y }  }{ \frac { 1 }{ x^{ 2 } } -\frac { 1 }{ y^{ 2 } }  } =\frac { \frac { 1 }{ x } +\frac { 1 }{ y }  }{ \left( \frac { 1 }{ x } +\frac { 1 }{ y }  \right) \left( \frac { 1 }{ x } -\frac { 1 }{ y }  \right)  } =\frac { 1 }{ \frac { 1 }{ x } -\frac { 1 }{ y }  } =\frac { 1 }{ \frac { y-x }{ xy }  } =\frac { xy }{ y-x } $$
