$\begin{array}{l}\phantom{\phantom{;}x^{2}-3x\phantom{;}+1;}{-3x^{3}-9x^{2}-22x\phantom{;}-57\phantom{;}\phantom{;}}\\\phantom{;}x^{2}-3x\phantom{;}+1\overline{\smash{)}-3x^{5}\phantom{-;x^n}+2x^{3}\phantom{-;x^n}+4x\phantom{;}-2\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x^{2}-3x\phantom{;}+1;}\underline{\phantom{;}3x^{5}-9x^{4}+3x^{3}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{\phantom{;}3x^{5}-9x^{4}+3x^{3};}-9x^{4}+5x^{3}\phantom{-;x^n}+4x\phantom{;}-2\phantom{;}\phantom{;}\\\phantom{\phantom{;}x^{2}-3x\phantom{;}+1-;x^n;}\underline{\phantom{;}9x^{4}-27x^{3}+9x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;\phantom{;}9x^{4}-27x^{3}+9x^{2}-;x^n;}-22x^{3}+9x^{2}+4x\phantom{;}-2\phantom{;}\phantom{;}\\\phantom{\phantom{;}x^{2}-3x\phantom{;}+1-;x^n-;x^n;}\underline{\phantom{;}22x^{3}-66x^{2}+22x\phantom{;}\phantom{-;x^n}}\\\phantom{;;\phantom{;}22x^{3}-66x^{2}+22x\phantom{;}-;x^n-;x^n;}-57x^{2}+26x\phantom{;}-2\phantom{;}\phantom{;}\\\phantom{\phantom{;}x^{2}-3x\phantom{;}+1-;x^n-;x^n-;x^n;}\underline{\phantom{;}57x^{2}-171x\phantom{;}+57\phantom{;}\phantom{;}}\\\phantom{;;;\phantom{;}57x^{2}-171x\phantom{;}+57\phantom{;}\phantom{;}-;x^n-;x^n-;x^n;}-145x\phantom{;}+55\phantom{;}\phantom{;}\\\end{array}$

$-3x^{3}-9x^{2}-22x-57+\frac{-145x+55}{x^2-3x+1}$