AMC 10 2014b Problem 9

For real numbers $w$ and $z$, $$\cfrac{\frac{1}{w} + \frac{1}{z}}{\frac{1}{w} - \frac{1}{z}} = 2014.$$ What is $\frac{w+z}{w-z}$? $\textbf{(A) }-2014 \textbf{(B) }\frac{-1}{2014} \textbf{(C) }\frac{1}{2014} \textbf{(D) }1 \textbf{(E) }2014$