1960 AHSME Problem 39

To satisfy the equation \frac{a+b}{a}=\frac{b}{a+b}, a and b must be:

\textbf{(A)}\ \text{both rational}\qquad\textbf{(B)}\ \text{both real but not rational}\qquad\textbf{(C)}\ \text{both not real}\qquad \textbf{(D)}\ \text{one real, one not real}\qquad\textbf{(E)}\ \text{one real, one not real or both not real}

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