Let $x_1, x_2, \ldots, x_n$ be the $n$ roots of the equation $x^n-3x^{n-1}+2x+1=0$. Calculate the sum $\sum_{k=1}^n \frac{x_k}{x_k-1}$.
Can somebody give me some tips, please? It's pretty hard to make up the sum using Vieta's formulas, and I think there may exist an easier method.