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

$3x^{3}-5x^{2}+5x-5+\frac{8}{x+1}$