Question 10

Algebra Level 3

\[ \large \dfrac{(x-1)(y-1)(z-1)}{(x-1)^3 + (y-1)^3 + (z-1)^3} \]

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

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