Q4 Matemática  (Balkan MO Shortlist 2011)

Seja $x,y,z\in {\mathbb{R}}^{+}$ satisfazendo $xyz=3(x+y+z)$. Prove que $$\begin{array}{r}\sum \frac{1}{x^2(y+1)}\ge \frac{3}{4(x+y+z)}\end{array}$$