Question 72
Suppose $x$ and $y$ are real numbers such that $-1 \lt x \lt y \lt 1$. Let $G$ be the sum of the geometric series whose first term is $x$ and whose ratio is $y$, and let $G'$ be the sum of the geometric series whose first term is $y$ and ratio is $x$. If $G = G'$, find $x + y$.