If $\frac {1}{x} - \frac {1}{y} = \frac {1}{z}$, then $z$ equals:
$\textbf{(A)}\ y - x\qquad \textbf{(B)}\ x - y\qquad \textbf{(C)}\ \frac {y - x}{xy}\qquad \textbf{(D)}\ \frac {xy}{y - x}\qquad \textbf{(E)}\ \frac {xy}{x - y}$
$\frac{1}{x}-\frac{1}{y}=\frac{1}{z}$
$\frac{y}{xy}-\frac{x}{xy}=\frac{1}{z}$
$\frac{y-x}{xy}=\frac{1}{z}$
$\frac{1}{\frac{y-x}{xy}}=\frac{1}{\frac{1}{z}}$
$\frac{xy}{y-x}=z$
The answer is therefore $\boxed{\text{D}}$.