AHSME 1960 Problem 39

To satisfy the equation $\frac{a+b}{a}=\frac{b}{a+b}$, $a$ and $b$ must be: $\textbf{(A)}\ \text{both rational} \textbf{(B)}\ \text{both real but not rational} \textbf{(C)}\ \text{both not real}$ $\textbf{(D)}\ \text{one real, one not real} \textbf{(E)}\ \text{one real, one not real or both not real}$