Inequality 1

Algebra Level 4

\[ \left( u+v+w \right) \left( {x}^{-1}+{y}^{-1}+{z}^{-1} \right) \left( {\frac {x}{u+v}}+{\frac {y}{v+w}}+{\frac {z}{w+u}} \right) \]

Let \(x,y,z,u,v,w>0\) ,and the minimum value of the expression is \(\frac{m} {n} \) for coprime positive integers \(m,n\), Evaluate \(m-n\).

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