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

$3x^{2}-4x+7+\frac{-8}{x+1}$