Question 114
Let $\mathbb{R}^* = \mathbb{R} \setminus \{0\}$ be the set of non-zero real numbers. Find all functions $f: \mathbb{R}^* \rightarrow \mathbb{R}^*$ satisfying
$$
f(x) + f(y) = f(x y f(x + y))
$$
for $x, y \in \mathbb{R}^*$ and $x + y \neq 0$.
$$
f(x) + f(y) = f(x y f(x + y))
$$
for $x, y \in \mathbb{R}^*$ and $x + y \neq 0$.