Help with simplifying an exponential equation

Question

$$\frac{x^3y^{-1}-y^3x^{-1}}{x^{-1}y+xy^{-1}}\cdot\frac{x^{-2}+y^{-2}}{xy^{-3}-x^{-3}y}$$

I need to simplify the above. Can anyone provide me with a step-by-step solution to this problem? I tried Wolfram but can't get the input to match up properly.

Answer 1

Using the induce rules, $a^{x}a^{y}=a^{x+y}$, I think you get $$\frac{xy^{-1}+x^{3}y^{-3}-y^{3}x^{-3}-yx^{-1}}{y^{-2}-y^{2}x^{-4}+x^{2}y^{-4}-x^{-2}}$$