CZ-SK-MO 1955 Problem 4

Given that $a,b,c$ are distinct real numbers, show that the equation $\frac{1}{x-a}+\frac{1}{x-b}+\frac{1}{x-c}=0$ has a real root.

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.