$\begin{array}{l}\phantom{\phantom{;}x\phantom{;}-1;}{\phantom{;}3x^{3}-4x^{2}+x\phantom{;}-9\phantom{;}\phantom{;}}\\\phantom{;}x\phantom{;}-1\overline{\smash{)}\phantom{;}3x^{4}-7x^{3}+5x^{2}-10x\phantom{;}+8\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x\phantom{;}-1;}\underline{-3x^{4}+3x^{3}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-3x^{4}+3x^{3};}-4x^{3}+5x^{2}-10x\phantom{;}+8\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}-1-;x^n;}\underline{\phantom{;}4x^{3}-4x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;\phantom{;}4x^{3}-4x^{2}-;x^n;}\phantom{;}x^{2}-10x\phantom{;}+8\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}-1-;x^n-;x^n;}\underline{-x^{2}+x\phantom{;}\phantom{-;x^n}}\\\phantom{;;-x^{2}+x\phantom{;}-;x^n-;x^n;}-9x\phantom{;}+8\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}-1-;x^n-;x^n-;x^n;}\underline{\phantom{;}9x\phantom{;}-9\phantom{;}\phantom{;}}\\\phantom{;;;\phantom{;}9x\phantom{;}-9\phantom{;}\phantom{;}-;x^n-;x^n-;x^n;}-1\phantom{;}\phantom{;}\\\end{array}$

$3x^{3}-4x^{2}+x-9+\frac{-1}{x-1}$