<s>[INST] Finding the range of $\frac{a}{b+c} + \frac{b}{c+a} + \frac{c}{a+b}$, for $a$, $b$, $c$ the sides of a triangle 
If $a$, $b$, and $c$ are the three sides of a triangle, then 
  $$\frac{a}{b+c} + \frac{b}{c+a} + \frac{c}{a+b}$$ 
  lies in what interval?

 [/INST] Since $a<b+c, b<c+a,c<a+b$ we have that 
$$
\frac{1}{b+c}\leq \frac{1}{a}, \frac{1}{c+a}\leq \frac{1}{b}, \leq \frac{1}{a+b}\leq \frac{1}{c},
$$
and 
$$
\frac{a}{b+c} + \frac{b}{c+a} + \frac{c}{a+b}\leq \frac{a}{a}+\frac{b}{b}+\frac{c}{c}=3
$$
</s>