AHSME 1952 Problem 7

When simplified, $(x^{-1}+y^{-1})^{-1}$ is equal to: $\textbf{(A) \ }x+y \textbf{(B) \ }\frac{xy}{x+y} \textbf{(C) \ }xy \textbf{(D) \ }\frac{1}{xy} \textbf{(E) \ }\frac{x+y}{xy}$