DE-MO 2017 Problem 5

Prove that for all non-negative numbers $x,y,z$ satisfying $x+y+z=1$ , one has $1 \le \frac{x}{1-yz}+\frac{y}{1-zx}+\frac{z}{1-xy} \le \frac{9}{8}.$

Dataset text AI-MO AoPS. Quoted with source.

Solutions

No solution is on olymmath yet. Official and human solutions come first when they arrive. AI solutions come after them, with a label.