MathNet 2012 Question 43

Let $f: \mathbb{R} \to \mathbb{R}$ be a function such that $f(x + y + xy) = f(x) + f(y) + f(xy)$ for all $x, y \in \mathbb{R}$. Prove that $f$ satisfies $f(x + y) = f(x) + f(y)$ for all $x, y \in \mathbb{R}$.