Question 99
Find all functions $f: \mathbb{Q}^{+} \rightarrow \mathbb{Q}$ such that
$$
f(x)+f(y)=\left(f(x+y)+\frac{1}{x+y}\right)(1-x y+f(x y))
$$
for all $x, y \in \mathbb{Q}^{+}$.
$$
f(x)+f(y)=\left(f(x+y)+\frac{1}{x+y}\right)(1-x y+f(x y))
$$
for all $x, y \in \mathbb{Q}^{+}$.