$\begin{array}{l}\phantom{\phantom{;}x\phantom{;}-1;}{\phantom{;}x^{2}+6x\phantom{;}-1\phantom{;}\phantom{;}}\\\phantom{;}x\phantom{;}-1\overline{\smash{)}\phantom{;}x^{3}+5x^{2}-7x\phantom{;}+3\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x\phantom{;}-1;}\underline{-x^{3}+x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-x^{3}+x^{2};}\phantom{;}6x^{2}-7x\phantom{;}+3\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}-1-;x^n;}\underline{-6x^{2}+6x\phantom{;}\phantom{-;x^n}}\\\phantom{;-6x^{2}+6x\phantom{;}-;x^n;}-x\phantom{;}+3\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}-1-;x^n-;x^n;}\underline{\phantom{;}x\phantom{;}-1\phantom{;}\phantom{;}}\\\phantom{;;\phantom{;}x\phantom{;}-1\phantom{;}\phantom{;}-;x^n-;x^n;}\phantom{;}2\phantom{;}\phantom{;}\\\end{array}$

$x^{2}+6x-1+\frac{2}{x-1}$