$\begin{array}{l}\phantom{\phantom{;}3x\phantom{;}-2;}{\phantom{;}3x^{3}+2x^{2}\phantom{-;x^n}-3\phantom{;}\phantom{;}}\\\phantom{;}3x\phantom{;}-2\overline{\smash{)}\phantom{;}9x^{4}\phantom{-;x^n}-4x^{2}-9x\phantom{;}+16\phantom{;}\phantom{;}}\\\phantom{\phantom{;}3x\phantom{;}-2;}\underline{-9x^{4}+6x^{3}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-9x^{4}+6x^{3};}\phantom{;}6x^{3}-4x^{2}-9x\phantom{;}+16\phantom{;}\phantom{;}\\\phantom{\phantom{;}3x\phantom{;}-2-;x^n;}\underline{-6x^{3}+4x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;-6x^{3}+4x^{2}-;x^n;}-9x\phantom{;}+16\phantom{;}\phantom{;}\\\phantom{\phantom{;}3x\phantom{;}-2-;x^n-;x^n;}\underline{\phantom{;}9x\phantom{;}-6\phantom{;}\phantom{;}}\\\phantom{;;\phantom{;}9x\phantom{;}-6\phantom{;}\phantom{;}-;x^n-;x^n;}\phantom{;}10\phantom{;}\phantom{;}\\\end{array}$

$3x^{3}+2x^{2}-3+\frac{10}{3x-2}$