# An algebra problem by Victor Loh

Algebra Level 3

Given that $$a,b,c$$ are positive reals such that the maximum value of $$N$$ which satisfies the inequality

$\frac{a}{b+c}+\frac{b}{a+c}+\frac{c}{a+b}\geq N$

can be expressed in the form $$\frac{m}{n}$$, where $$m$$ and $$n$$ are coprime, positive integers, find the value of $$m+n$$.

$$\textbf{Details and Assumptions}$$

For those who know a certain inequality, this problem is going to be a no-brainer. :D

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