How can I simplify this expression 
I know that I cannot just do $\frac{x^{-1}}{x^{-3}}$ and $\frac{y^{-1}}{y^{-3}}$ and get $x^{2}+y^{2}$ but how can i factor either the numerator or denominator to get something to cancel out?

$\dfrac{x^{-1}+y^{-1}}{x^{-3}+y^{-3}}=\dfrac{x^3y^3(x^{-1}+y^{-1})}{x^3y^3(x^{-3}+y^{-3})}= \dfrac{x^{2}y^3+x^3y^{2}}{x^{3}+y^{3}}=\dfrac{(x^2y^2)(x+y)}{x^{3}+y^{3}}=\dfrac{(x^2y^2)(x+y)}{(x+y)(x^2-xy+y^2)}=\dfrac{(x^2y^2)}{(x^2-xy+y^2)}$
