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Easy algebra

Source: Kyiv City MO 2022 Round 2, Problem 10.1

January 30, 2022
algebrainequalitiesUkraine

Problem Statement

Positive reals x,y,zx, y, z satisfy xy+1x+1=yz+1y+1=zx+1z+1\frac{xy+1}{x+1} = \frac{yz+1}{y+1} = \frac{zx+1}{z+1}
Do they all have to be equal?
(Proposed by Oleksii Masalitin)
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