# Welcome 2016! Part 6

Algebra Level 4

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

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

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