Školjka

%V0 Let $a$, $b$, $c$ be positive real numbers such that $abc = 1$. Prove that $$\frac {1}{a^{3}\left(b + c\right)} + \frac {1}{b^{3}\left(c + a\right)} + \frac {1}{c^{3}\left(a + b\right)}\geq \frac {3}{2}.$$