[tex]\left (\cfrac{1}{x}+\cfrac{1}{y} \right )^2\cdot (x+y)^{-2}=\left ( \cfrac{y+x}{xy} \right )^2\cdot \cfrac{1}{(x+y)^2}=\cfrac{(y+x)^2}{(xy)^2}\cdot \cfrac{1}{(x+y)^2}=\cfrac{1}{(xy)^2}[/tex]