ÖMO 1990 Problem 5

Determine all rational numbers $r$ such that all solutions of the equation:

$rx^2+(r+1)x+(r-1)=0$ are integers.

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.