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Regional Olympiad - FBH 2012 Grade 12 Problem 4

Source: Regional Olympiad - Federation of Bosnia and Herzegovina 2012

September 25, 2018

inequalitiesalgebra

Problem Statement

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