An algebra problem by Victor Loh

Algebra Level 3

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

ab+c+ba+c+ca+bN\frac{a}{b+c}+\frac{b}{a+c}+\frac{c}{a+b}\geq N

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

Details and Assumptions\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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