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Inequality in three fractions

Source: Problem 4 of Russian Regional Olympiad 2011, grade 9

September 1, 2011
inequalitiescalculusthree variable inequality

Problem Statement

xx, yy and zz are positive real numbers. Prove the inequality x+1y+1+y+1z+1+z+1x+1≤xy+yz+zx.\frac{x+1}{y+1}+\frac{y+1}{z+1}+\frac{z+1}{x+1}\leq\frac{x}{y}+\frac{y}{z}+\frac{z}{x}. (Authors: A. Khrabrov, B. Trushin)
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