International Mathematical Olympiad 1994 Problem 5

Let $S$ be the set of real numbers strictly greater than $-1$. Find all functions $f: S \to S$ satisfying the two conditions:

1. $f(x + f(y) + xf(y)) = y + f(x) + yf(x)$ for all $x$ and $y$ in $S$;
2. $\frac{f(x)}{x}$ is strictly increasing on each of the intervals $-1 < x < 0$ and $0 < x$.