Problem

Source: 2011 Saudi Arabia BMO TST 2.3 - Balkan MO

Tags: algebra, inequalities



Let $a, b, c$ be positive real numbers. Prove that $$\frac{1}{a+b+\frac{1}{abc}+1}+\frac{1}{b+c+\frac{1}{abc}+1}+\frac{1}{c+a+\frac{1}{abc}+1}\le \frac{a + b + c}{a+b+c+1}$$