$\begin{array}{l}\phantom{\phantom{;}x\phantom{;}-1;}{\phantom{;}x^{2}-5x\phantom{;}+4\phantom{;}\phantom{;}}\\\phantom{;}x\phantom{;}-1\overline{\smash{)}\phantom{;}x^{3}-6x^{2}+9x\phantom{;}-1\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x\phantom{;}-1;}\underline{-x^{3}+x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-x^{3}+x^{2};}-5x^{2}+9x\phantom{;}-1\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}-1-;x^n;}\underline{\phantom{;}5x^{2}-5x\phantom{;}\phantom{-;x^n}}\\\phantom{;\phantom{;}5x^{2}-5x\phantom{;}-;x^n;}\phantom{;}4x\phantom{;}-1\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}-1-;x^n-;x^n;}\underline{-4x\phantom{;}+4\phantom{;}\phantom{;}}\\\phantom{;;-4x\phantom{;}+4\phantom{;}\phantom{;}-;x^n-;x^n;}\phantom{;}3\phantom{;}\phantom{;}\\\end{array}$

$x^{2}-5x+4+\frac{3}{x-1}$