UA-UMO 2005 Problem 81

Find all pairs of real numbers $(x,y)$ such that:

$\frac{x-2}{y}+\frac{5}{xy}=\frac{4-y}{x}-\frac{|y-2x|}{xy}.$

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.