Question 32
Let $x$, $y$ and $z$ be real numbers in the interval $(-1, 1)$. Prove that
$$
\frac{1}{(1-x^2)(1-y^2)(1-z^2)} + \frac{2}{(1-xy)(1-yz)(1-zx)} \geq
\frac{1}{(1-x^2)(1-yz)^2} + \frac{1}{(1-y^2)(1-zx)^2} + \frac{1}{(1-z^2)(1-xy)^2}.
$$
$$
\frac{1}{(1-x^2)(1-y^2)(1-z^2)} + \frac{2}{(1-xy)(1-yz)(1-zx)} \geq
\frac{1}{(1-x^2)(1-yz)^2} + \frac{1}{(1-y^2)(1-zx)^2} + \frac{1}{(1-z^2)(1-xy)^2}.
$$