$\begin{array}{l}\phantom{\phantom{;}3x^{2}+x\phantom{;}+1;}{-2x\phantom{;}+7\phantom{;}\phantom{;}}\\\phantom{;}3x^{2}+x\phantom{;}+1\overline{\smash{)}-6x^{3}+19x^{2}+8x\phantom{;}+12\phantom{;}\phantom{;}}\\\phantom{\phantom{;}3x^{2}+x\phantom{;}+1;}\underline{\phantom{;}6x^{3}+2x^{2}+2x\phantom{;}\phantom{-;x^n}}\\\phantom{\phantom{;}6x^{3}+2x^{2}+2x\phantom{;};}\phantom{;}21x^{2}+10x\phantom{;}+12\phantom{;}\phantom{;}\\\phantom{\phantom{;}3x^{2}+x\phantom{;}+1-;x^n;}\underline{-21x^{2}-7x\phantom{;}-7\phantom{;}\phantom{;}}\\\phantom{;-21x^{2}-7x\phantom{;}-7\phantom{;}\phantom{;}-;x^n;}\phantom{;}3x\phantom{;}+5\phantom{;}\phantom{;}\\\end{array}$

$-2x+7+\frac{3x+5}{3x^2+x+1}$