# 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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