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Algebra Level 4

\[P(x) = x^{3}-2007x+2002\]

Given that \(r\), \(s\) and \(t\) are all real roots of the above polynomial, find \(\dfrac{r-1}{r+1}+\dfrac{s-1}{s+1}+\dfrac{t-1}{t+1}\) .

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