Question 140
Find all functions $f: \mathbb{R} \rightarrow \mathbb{R}$ satisfying $f(x)+f(y) \neq 0$ and
$$
\frac{f(x)-f(x-y)}{f(x)+f(x+y)}+\frac{f(x)-f(x+y)}{f(x)+f(x-y)}=0
$$
for all $x, y \in \mathbb{R}$.
$$
\frac{f(x)-f(x-y)}{f(x)+f(x+y)}+\frac{f(x)-f(x+y)}{f(x)+f(x-y)}=0
$$
for all $x, y \in \mathbb{R}$.