Školjka

Let $\mathbb{Q}^+$ denote the set of all positive rational numbers and let $\alpha \in \mathbb{Q}^+$. Determine all functions $f : \mathbb{Q}^+ \rightarrow (\alpha, +\infty)$ such that $$f\bigg(\frac{x+y}{\alpha}\bigg) = \frac{f(x)+f(y)}{\alpha}$$ for all $x, y \in \mathbb{Q}^+$