IMO Shortlist 1995 problem A1

Let $a$ , $b$ , $c$ be positive real numbers such that $abc = 1$ . Prove that $\frac {1}{a^{3}\left(b + c\right)} + \frac {1}{b^{3}\left(c + a\right)} + \frac {1}{c^{3}\left(a + b\right)}\geq \frac {3}{2}.$

Source: Međunarodna matematička olimpijada, shortlist 1995

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IMO Shortlist 1995 problem A1