MathNet 2020 — Math Olympiad Vault — Part 01 Question 68

Let $a$, $b$, $c$ be positive real numbers with $abc = 1$. Prove that
$$
\frac{a}{b(c+1)} + \frac{b}{c(a+1)} + \frac{c}{a(b+1)} \ge \frac{3}{2}.
$$