Too many x,y,z

Algebra Level 4

If \(x+y+z=0 \), simplify

\[ \left( \dfrac{x-y}z + \dfrac{y-z}x + \dfrac{z-x}y \right)\left( \dfrac z{x-y} + \dfrac x{y-z} + \dfrac y{z-x} \right). \]

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