Let $a, b, c$ be positive reals. Prove that $a/b+b/c+c/a=>(c+a)/(c+b) + (a+b)/(a+c) + (b+c)/(b+a)$
Source: Saudi Arabia JBMO training test 6, 2019, P4
Tags: inequalities
Let $a, b, c$ be positive reals. Prove that $a/b+b/c+c/a=>(c+a)/(c+b) + (a+b)/(a+c) + (b+c)/(b+a)$