Question 129
Find all functions $f: \mathbb{Q}^+ \to \mathbb{Q}$ satisfying
$$
f(x) + f(y) = \left( f(x + y) + \frac{1}{x + y} \right) (1 - xy + f(xy))
$$
for all $x, y \in \mathbb{Q}^+$.
$$
f(x) + f(y) = \left( f(x + y) + \frac{1}{x + y} \right) (1 - xy + f(xy))
$$
for all $x, y \in \mathbb{Q}^+$.