UA-UMO 1998 Problem 113

For any numbers $0<x,y,z\le1$ prove the inequality $\frac x{1+y+zx}+\frac y{1+z+xy}+\frac z{1+x+yz}\le\frac3{x+y+z}.$

Dataset text AI-MO AoPS. Quoted with source.

Solutions

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