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

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