Algebra Question by Mithil Shah # 1

Algebra Level 3

Find positive integers \(x,y,z\) such that \(x \lt y \lt z\) and

\[\dfrac{1}{x} - \dfrac{1}{xy} - \dfrac{1}{xyz} = \dfrac{19}{97}\]

Determine the value of \(x+y+z\).

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