Question

(х^-1-у^-1)(х-у)^-1=?

Answer 1

=(1/x-1/y)×1/(x-y)=(y-x)/xy×(-1/(y-x))=-1/xy

Answer 2

$(x^{-1}-y^{-1})(x-y)^{-1} = (frac{1}{x}- frac{1}{y} )( frac{1}{x-y} ) = frac{1}{x} ( frac{1}{x-y} ) - frac{1}{y} ( frac{1}{x-y} ) =$
$= frac{1}{x(x-y)} - frac{1}{y(x-y)} = frac{y-x}{xy(x-y)} =- frac{x-y}{xy(x-y)} = - frac{1}{xy}$