Školjka

%V0 Let $x,y$ and $z$ be positive real numbers such that $xyz=1$. Prove that $$\frac{x^{3}}{(1 + y)(1 + z)}+\frac{y^{3}}{(1 + z)(1 + x)}+\frac{z^{3}}{(1 + x)(1 + y)} \geq \frac{3}{4}.$$