AHSME 1951 Problem 20

When simplified and expressed with negative exponents, the expression $(x + y)^{ - 1}(x^{ - 1} + y^{ - 1})$ is equal to: $\textbf{(A)}\ x^{ - 2} + 2x^{ - 1}y^{ - 1} + y^{ - 2} \textbf{(B)}\ x^{ - 2} + 2^{ - 1}x^{ - 1}y^{ - 1} + y^{ - 2} \textbf{(C)}\ x^{ - 1}y^{ - 1}$ $\textbf{(D)}\ x^{ - 2} + y^{ - 2} \textbf{(E)}\ \frac {1}{x^{ - 1}y^{ - 1}}$