For any numbers $0<x,y,z\le1$ prove the inequality $$\frac x{1+y+zx}+\frac y{1+z+xy}+\frac z{1+x+yz}\le\frac3{x+y+z}.$$
Source: Ukraine 1998 Grade 11 P3
Tags: inequalities
For any numbers $0<x,y,z\le1$ prove the inequality $$\frac x{1+y+zx}+\frac y{1+z+xy}+\frac z{1+x+yz}\le\frac3{x+y+z}.$$