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# help

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Let $$a,b,c$$ be the sides of a triangle. Find the set of all possible values of $$\frac{a}{b + c} + \frac{b}{a + c} + \frac{c}{a + b}.$$

Mar 8, 2019
edited by Guest  Mar 8, 2019

$$\text{The expression seems to vary from }\dfrac 3 2\\ \text{which corresponds to an equilateral triangle to }2\\ \text{which corresponds to an isosceles triangle with one leg having zero length}\\ \dfrac 3 2 \leq \dfrac{a}{b+c}+ \dfrac{b}{a+c}+\dfrac{c}{a+b} < 2$$