1963 AHSME Problem 17

The expression \dfrac{\dfrac{a}{a+y}+\dfrac{y}{a-y}}{\dfrac{y}{a+y}-\dfrac{a}{a-y}}, a real, a\neq 0, has the value -1 for:

\begin{array}{l} \textbf{(A)}\ \text{all but two real values of }y \qquad \\ \textbf{(B)}\ \text{only two real values of }y \qquad \\ \textbf{(C)}\ \text{all real values of }y\qquad \\ \textbf{(D)}\ \text{only one real value of }y\qquad \\ \textbf{(E)}\ \text{no real values of }y \end{array}

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.