$\begin{array}{l}\phantom{\phantom{;}x\phantom{;}+1;}{\phantom{;}3x^{3}-3x^{2}+x\phantom{;}+6\phantom{;}\phantom{;}}\\\phantom{;}x\phantom{;}+1\overline{\smash{)}\phantom{;}3x^{4}\phantom{-;x^n}-2x^{2}+7x\phantom{;}-3\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x\phantom{;}+1;}\underline{-3x^{4}-3x^{3}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-3x^{4}-3x^{3};}-3x^{3}-2x^{2}+7x\phantom{;}-3\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+1-;x^n;}\underline{\phantom{;}3x^{3}+3x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;\phantom{;}3x^{3}+3x^{2}-;x^n;}\phantom{;}x^{2}+7x\phantom{;}-3\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+1-;x^n-;x^n;}\underline{-x^{2}-x\phantom{;}\phantom{-;x^n}}\\\phantom{;;-x^{2}-x\phantom{;}-;x^n-;x^n;}\phantom{;}6x\phantom{;}-3\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+1-;x^n-;x^n-;x^n;}\underline{-6x\phantom{;}-6\phantom{;}\phantom{;}}\\\phantom{;;;-6x\phantom{;}-6\phantom{;}\phantom{;}-;x^n-;x^n-;x^n;}-9\phantom{;}\phantom{;}\\\end{array}$

$3x^{3}-3x^{2}+x+6+\frac{-9}{x+1}$