Middle European Mathematical Olympiad 2018 Problem T-1

Let $a$, $b$ and $c$ be positive real numbers satisfying $abc = 1$. Prove that $$\frac{a^2 - b^2}{a + bc} + \frac{b^2 - c^2}{b + ca} + \frac{c^2 - a^2}{c + ab} \leq a + b + c - 3.$$