(х^-1-у^-1)(х-у)^-1=?

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

[latex](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} ) =[/latex] [latex]= \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} [/latex]