$\begin{array}{l}\phantom{\phantom{;}x\phantom{;}-1;}{\phantom{;}x^{2}-3x\phantom{;}-2\phantom{;}\phantom{;}}\\\phantom{;}x\phantom{;}-1\overline{\smash{)}\phantom{;}x^{3}-4x^{2}+x\phantom{;}+6\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x\phantom{;}-1;}\underline{-x^{3}+x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-x^{3}+x^{2};}-3x^{2}+x\phantom{;}+6\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}-1-;x^n;}\underline{\phantom{;}3x^{2}-3x\phantom{;}\phantom{-;x^n}}\\\phantom{;\phantom{;}3x^{2}-3x\phantom{;}-;x^n;}-2x\phantom{;}+6\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}-1-;x^n-;x^n;}\underline{\phantom{;}2x\phantom{;}-2\phantom{;}\phantom{;}}\\\phantom{;;\phantom{;}2x\phantom{;}-2\phantom{;}\phantom{;}-;x^n-;x^n;}\phantom{;}4\phantom{;}\phantom{;}\\\end{array}$

$x^{2}-3x-2+\frac{4}{x-1}$