IMO 1995 — Shortlisted problems Question 1

A1 (RUS), IMO2. Let $a$, $b$, and $c$ be positive real numbers such that $abc=1$. Prove that
$$\frac1{a^3(b+c)}+\frac1{b^3(a+c)}+\frac1{c^3(a+b)}\ge\frac32.$$