$\begin{array}{l}\phantom{\phantom{;}3x\phantom{;}+1;}{\phantom{;}4x^{2}+2x\phantom{;}+3\phantom{;}\phantom{;}}\\\phantom{;}3x\phantom{;}+1\overline{\smash{)}\phantom{;}12x^{3}+10x^{2}+11x\phantom{;}+12\phantom{;}\phantom{;}}\\\phantom{\phantom{;}3x\phantom{;}+1;}\underline{-12x^{3}-4x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-12x^{3}-4x^{2};}\phantom{;}6x^{2}+11x\phantom{;}+12\phantom{;}\phantom{;}\\\phantom{\phantom{;}3x\phantom{;}+1-;x^n;}\underline{-6x^{2}-2x\phantom{;}\phantom{-;x^n}}\\\phantom{;-6x^{2}-2x\phantom{;}-;x^n;}\phantom{;}9x\phantom{;}+12\phantom{;}\phantom{;}\\\phantom{\phantom{;}3x\phantom{;}+1-;x^n-;x^n;}\underline{-9x\phantom{;}-3\phantom{;}\phantom{;}}\\\phantom{;;-9x\phantom{;}-3\phantom{;}\phantom{;}-;x^n-;x^n;}\phantom{;}9\phantom{;}\phantom{;}\\\end{array}$

$4x^{2}+2x+3+\frac{9}{3x+1}$