Prove that $\frac{1}{x(1-y)} +\frac{1}{y(1-z)} +\frac{1}{z(1-x)} \ge \frac{3}{xyz+(1-x)(1-y)(1-z)} $ Let $x,y,z$ be real numbers in the range of $(0,1)$.
Prove that
$$\frac{1}{x(1-y)} +\frac{1}{y(1-z)} +\frac{1}{z(1-x)} \ge \frac{3}{xyz+(1-x)(1-y)(1-z)}.$$

It's obviously true after following substitution and full expanding.
$x=\frac{a}{a+1}$, $y=\frac{b}{b+1}$ and $z=\frac{c}{c+1}$, where $a$, $b$ and $c$ are positives.
