# How do you simplify [x^-1+y^-1]/[x^-2-y^-2]?

Jul 25, 2016

$x - y$

#### Explanation:

This one is interesting in that its set to look tricky but its not really that bad as it seems.

Firs we know that ${z}^{-} x = \frac{1}{{z}^{x}}$ and also ${z}^{-} \left(- x\right) = \frac{1}{{z}^{-} x} = {z}^{x}$

so lets rearrange this equation

$\frac{{x}^{2} - {y}^{2}}{{x}^{1} + {y}^{1}}$

now it turns out that
$\left(x - y\right) \left(x + y\right) = \left({x}^{2} - {y}^{2}\right)$

so we have
$\frac{\left(x - y\right) \cancel{x + y}}{\cancel{x + y}}$