Question 32
Let $\alpha \in \mathbb{Q}^+$. Determine all functions $f: \mathbb{Q}^+ \to \mathbb{Q}^+$ such that
$$
f\left(\frac{x}{y} + y\right) = \frac{f(x)}{f(y)} + f(y) + \alpha x
$$
holds for all $x, y \in \mathbb{Q}^+$.
Here, $\mathbb{Q}^+$ denotes the set of positive rational numbers.
$$
f\left(\frac{x}{y} + y\right) = \frac{f(x)}{f(y)} + f(y) + \alpha x
$$
holds for all $x, y \in \mathbb{Q}^+$.
Here, $\mathbb{Q}^+$ denotes the set of positive rational numbers.