FKMO 2016 Problem 3

Prove that for all rationals $x,y$ , $x-\frac{1}{x}+y-\frac{1}{y}=4$ is not true.

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.