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