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INMO 1990 Problem 5

    Let aa , bb , cc denote the sides of a triangle. Show that the quantity ab+c+bc+a+ca+b\frac{a}{b+c}+\frac{b}{c+a}+\frac{c}{a+b} must lie between the limits 3/23/2 and 2. Can equality hold at either limits?

    Dataset text AI-MO AoPS. Quoted with source.

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