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Bosnia and Herzegovina JBMO TST 2011 Problem 2

Source: Bosnia and Herzegovina Junior Balkan Mathematical Olympiad TST 2011

September 16, 2018

nonnegativeInequalityinequalities

Problem Statement

Prove inequality, with

a

and

b

nonnegative real numbers:

\frac{a+b}{1+a+b}\leq \frac{a}{1+a} + \frac{b}{1+b} \leq \frac{2(a+b)}{2+a+b}