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a/(b + 1)+b/(a + 1)<=1 if 0<=a, b<= 1

Source: Austria Beginners' Competition 2013 p3

October 3, 2021
algebrainequalities

Problem Statement

Let aa and b b be real numbers with 0≤a,b≤10\le a, b\le 1. Prove that ab+1+ba+1≤1\frac{a}{b + 1}+\frac{b}{a + 1}\le 1 When does equality holds?
(K. Czakler, GRG 21, Vienna)
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