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