NMTC Practice Part 9

If \(x\), \(y\), \(z\) are distinct natural number such that \(x<y<z\) and \(\frac{1}{x}-\frac{1}{xy}-\frac{1}{xyz}=\frac{19}{97}\), then find \(x+y+z\).

Part of the set NMTC Practice Problems.
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