abc of maths

Algebra Level 3

If \[\frac{a}{b+c} + \frac{b}{a+c} + \frac{c}{a+b} = 0\] and \(a+b+c = 5\), the value of \[\frac{1}{b+c} + \frac{1}{a+c} + \frac{1}{a+b}\] can be expressed in the form \(\frac{m}{n}\), where \(m\) and \(n\) are coprime, positive integers. Find the value of \(m+n\).

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