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Proof of inequality

Source: Japan Mathematical Olympiad Finals 2004, Problem 4

March 30, 2005
inequalitiesinequalities proposed

Problem Statement

For positive real numbers a,b,ca,b,c satisfying a+b+c=1,a+b+c=1, Prove that we have 1+a1−a+1+b1−b+1+c1−c≦2(ba+cb+ac).\frac{1+a}{1-a}+\frac{1+b}{1-b}+\frac{1+c}{1-c}\leqq 2\left(\frac{b}{a}+\frac{c}{b}+\frac{a}{c}\right). Note that you don't need to state for the condition for which the equality holds.
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