VMO 2021 Problem 2

Find all function $f:\mathbb{R}\to \mathbb{R}$ such that $f(x)f(y)=f(xy-1)+yf(x)+xf(y)$ for all $x,y \in \mathbb{R}$

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.