Not so easy

Algebra Level 3

ab+c+ba+c+ca+b \dfrac a{b+c} + \dfrac b{a+c} + \dfrac c{a+b}

If a,ba,b and cc are positive real numbers, find the minimum value of the expression above. If this value can be expressed as mn\dfrac mn, where mm and nn are coprime positive integers, submit m+nm+n as your answer.

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