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

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