Inspect polynomial

Algebra Level 4

P(x)=x32007x+2002P(x) = x^{3}-2007x+2002

Given that rr, ss and tt are all real roots of the above polynomial, find r1r+1+s1s+1+t1t+1\dfrac{r-1}{r+1}+\dfrac{s-1}{s+1}+\dfrac{t-1}{t+1} .

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