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

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