# 19 and 97 are primes right?

Number Theory Level 4

Find positive integers $$x,y,z$$ satisfying $$x<y<z$$ and $$\dfrac{1}{x}-\dfrac{1}{xy}-\dfrac{1}{xyz}=\dfrac{19}{97}$$.

Submit your answer as the value of $$x+y+z$$.

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