$\begin{array}{l}\phantom{\phantom{;}3x^{3}+2x\phantom{;}+1;}{\phantom{;}4x^{2}-2x\phantom{;}+2\phantom{;}\phantom{;}}\\\phantom{;}3x^{3}+2x\phantom{;}+1\overline{\smash{)}\phantom{;}12x^{5}-6x^{4}+14x^{3}-30x^{2}+16x\phantom{;}+9\phantom{;}\phantom{;}}\\\phantom{\phantom{;}3x^{3}+2x\phantom{;}+1;}\underline{-12x^{5}\phantom{-;x^n}-8x^{3}-4x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-12x^{5}-8x^{3}-4x^{2};}-6x^{4}+6x^{3}-34x^{2}+16x\phantom{;}+9\phantom{;}\phantom{;}\\\phantom{\phantom{;}3x^{3}+2x\phantom{;}+1-;x^n;}\underline{\phantom{;}6x^{4}\phantom{-;x^n}+4x^{2}+2x\phantom{;}\phantom{-;x^n}}\\\phantom{;\phantom{;}6x^{4}+4x^{2}+2x\phantom{;}-;x^n;}\phantom{;}6x^{3}-30x^{2}+18x\phantom{;}+9\phantom{;}\phantom{;}\\\phantom{\phantom{;}3x^{3}+2x\phantom{;}+1-;x^n-;x^n;}\underline{-6x^{3}\phantom{-;x^n}-4x\phantom{;}-2\phantom{;}\phantom{;}}\\\phantom{;;-6x^{3}-4x\phantom{;}-2\phantom{;}\phantom{;}-;x^n-;x^n;}-30x^{2}+14x\phantom{;}+7\phantom{;}\phantom{;}\\\end{array}$

$4x^{2}-2x+2+\frac{-30x^{2}+14x+7}{3x^3+2x+1}$