Welcome 2016! Part 6

Algebra Level 4

aba+b=3 , bcb+c=4 , cac+a=5\dfrac{ab}{a+b}=3 \ , \ \dfrac{bc}{b+c}=4 \ , \ \dfrac{ca}{c+a}=5

Let a,ba,b and cc be real numbers satisfying all 3 equations above. Given that abcab+ac+bc \dfrac{abc}{ab+ac+bc} is equal to mn \dfrac mn, where mm and nn are coprime positive integers, find the value of m+nm+n.

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