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sum (1+a)/(1+a+ab) where abc=1

Source: Switzerland - 2005 Swiss MO Final Round p6

December 26, 2022
algebraSum

Problem Statement

Let a,b,ca, b, c be positive real numbers with abc=1abc = 1. Find all possible values ​​of the expression 1+a1+a+ab+1+b1+b+bc+1+c1+c+ca\frac{1 + a}{1 + a + ab}+\frac{1 + b}{1 + b + bc}+\frac{1 + c}{1 + c + ca} can take.
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