Prove the inequality: $$\frac{A+a+B+b}{A+a+B+b+c+r}+\frac{B+b+C+c}{B+b+C+c+a+r}>\frac{C+c+A+a}{C+c+A+a+b+r}$$where $A$, $B$, $C$, $a$, $b$, $c$ and $r$ are positive real numbers
Problem
Source: Regional Olympiad - Federation of Bosnia and Herzegovina 2012
Tags: inequalities, algebra