$\begin{array}{l}\phantom{\phantom{;}3x\phantom{;}+2;}{\phantom{;}81x^{2}-54x\phantom{;}+36\phantom{;}\phantom{;}}\\\phantom{;}3x\phantom{;}+2\overline{\smash{)}\phantom{;}243x^{3}\phantom{-;x^n}\phantom{-;x^n}+32\phantom{;}\phantom{;}}\\\phantom{\phantom{;}3x\phantom{;}+2;}\underline{-243x^{3}-162x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-243x^{3}-162x^{2};}-162x^{2}\phantom{-;x^n}+32\phantom{;}\phantom{;}\\\phantom{\phantom{;}3x\phantom{;}+2-;x^n;}\underline{\phantom{;}162x^{2}+108x\phantom{;}\phantom{-;x^n}}\\\phantom{;\phantom{;}162x^{2}+108x\phantom{;}-;x^n;}\phantom{;}108x\phantom{;}+32\phantom{;}\phantom{;}\\\phantom{\phantom{;}3x\phantom{;}+2-;x^n-;x^n;}\underline{-108x\phantom{;}-72\phantom{;}\phantom{;}}\\\phantom{;;-108x\phantom{;}-72\phantom{;}\phantom{;}-;x^n-;x^n;}-40\phantom{;}\phantom{;}\\\end{array}$

$81x^{2}-54x+36+\frac{-40}{3x+2}$