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Part of 2011 Bosnia and Herzegovina Junior BMO TST

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Bosnia and Herzegovina JBMO TST 2011 Problem 2

Source: Bosnia and Herzegovina Junior Balkan Mathematical Olympiad TST 2011

9/16/2018
Prove inequality, with aa and bb nonnegative real numbers: a+b1+a+b≤a1+a+b1+b≤2(a+b)2+a+b\frac{a+b}{1+a+b}\leq \frac{a}{1+a} + \frac{b}{1+b} \leq \frac{2(a+b)}{2+a+b}
nonnegativeInequalityinequalities