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Japanese ineq

Source: Japan MO; posted by Zhaobin in Pre-Olympiad section

February 5, 2005
inequalitiesfunction3-variable inequalityNesbittGermanyJapan

Problem Statement

If aa, bb, cc are positive reals such that a+b+c=1a+b+c=1, prove that
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}\leq 2\left(\frac{b}{a}+\frac{c}{b}+\frac{a}{c}\right).
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