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\frac{a- b}{b +c}+\frac{b- c}{c +d}+\frac{c - d}{d +a} +\frac{d - a}{a + b}>=0

Source: Dutch IMO TST1 2012 p2

January 10, 2020
inequalities

Problem Statement

Let a,b,ca, b, c and dd be positive real numbers. Prove that a−bb+c+b−cc+d+c−dd+a+d−aa+b≥0\frac{a - b}{b + c}+\frac{b - c}{c + d}+\frac{c - d}{d + a} +\frac{d - a}{a + b } \ge 0
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