Question 170
Prove that for positive real numbers $x, y, z$ the following inequality is satisfied:
$$
\frac{1+xy+xz}{(1+y+z)^2} + \frac{1+yz+yx}{(1+z+x)^2} + \frac{1+zx+zy}{(1+x+y)^2} \ge 1
$$
$$
\frac{1+xy+xz}{(1+y+z)^2} + \frac{1+yz+yx}{(1+z+x)^2} + \frac{1+zx+zy}{(1+x+y)^2} \ge 1
$$