Question 10

Algebra Level 3

(x1)(y1)(z1)(x1)3+(y1)3+(z1)3 \large \dfrac{(x-1)(y-1)(z-1)}{(x-1)^3 + (y-1)^3 + (z-1)^3}

If x+y+z=3x+y+z=3 and the value of the above expression can be expressed as 1n\dfrac{1}{n} for some positive integer nn, find nn.

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