Can anyone explain how to get [(x+y)/(xy)] as a solution for [(x{^-2} - y{^-2}) / (x{^-1} - y{^-1})]?

I have tried different ways of doing it but I still keep getting [(x-y) / (xy)] every time. If you could explain step by step, that would be great!

Start by multiplying both numerator and denominator by \small{x^2y^2}:


\frac {( \frac 1 {x^2}-\frac 1 {y^2})} {( \frac 1 x - \frac 1 y) } \cdot \frac {x^2y^2}{x^2y^2} = \frac {y^2 - x^2}{xy^2 - x^2y} = \frac {(y-x)(y+x)} {xy(y-x)} = \frac {y+x} {xy}