Question 164
Let $x$, $y$, $z$ be real numbers such that $x \in (0, 1]$, $y \in (0, 1]$, $z \in (0, 1]$. Prove the inequality:
$$
\frac{x}{2+xy+yz} + \frac{y}{2+yz+zx} + \frac{z}{2+zx+xy} \le \frac{x+y+z}{x+y+z+xyz}
$$
$$
\frac{x}{2+xy+yz} + \frac{y}{2+yz+zx} + \frac{z}{2+zx+xy} \le \frac{x+y+z}{x+y+z+xyz}
$$