$\begin{array}{l}\phantom{\phantom{;}x\phantom{;}+1;}{\phantom{;}3x^{2}+3x\phantom{;}-4\phantom{;}\phantom{;}}\\\phantom{;}x\phantom{;}+1\overline{\smash{)}\phantom{;}3x^{3}+6x^{2}-x\phantom{;}+2\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x\phantom{;}+1;}\underline{-3x^{3}-3x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-3x^{3}-3x^{2};}\phantom{;}3x^{2}-x\phantom{;}+2\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+1-;x^n;}\underline{-3x^{2}-3x\phantom{;}\phantom{-;x^n}}\\\phantom{;-3x^{2}-3x\phantom{;}-;x^n;}-4x\phantom{;}+2\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+1-;x^n-;x^n;}\underline{\phantom{;}4x\phantom{;}+4\phantom{;}\phantom{;}}\\\phantom{;;\phantom{;}4x\phantom{;}+4\phantom{;}\phantom{;}-;x^n-;x^n;}\phantom{;}6\phantom{;}\phantom{;}\\\end{array}$

$3x^{2}+3x-4+\frac{6}{x+1}$