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

$3x^{2}-8x+8+\frac{-4}{x+1}$