AHSME 1979 Problem 2

For all non-zero real numbers $x$ and $y$ such that $x-y=xy, \frac{1}{x}-\frac{1}{y}$ equals $\textbf{(A) }\frac{1}{xy} \textbf{(B) }\frac{1}{x-y} \textbf{(C) }0 \textbf{(D) }-1 \textbf{(E) }y-x$