$\begin{array}{l}\phantom{\phantom{;}3x^{2}+2;}{\phantom{;}x\phantom{;}+\frac{2}{3}\phantom{;}\phantom{;}}\\\phantom{;}3x^{2}+2\overline{\smash{)}\phantom{;}3x^{3}+2x^{2}+x\phantom{;}-5\phantom{;}\phantom{;}}\\\phantom{\phantom{;}3x^{2}+2;}\underline{-3x^{3}\phantom{-;x^n}-2x\phantom{;}\phantom{-;x^n}}\\\phantom{-3x^{3}-2x\phantom{;};}\phantom{;}2x^{2}-x\phantom{;}-5\phantom{;}\phantom{;}\\\phantom{\phantom{;}3x^{2}+2-;x^n;}\underline{-2x^{2}\phantom{-;x^n}-\frac{4}{3}\phantom{;}\phantom{;}}\\\phantom{;-2x^{2}-\frac{4}{3}\phantom{;}\phantom{;}-;x^n;}-x\phantom{;}-\frac{19}{3}\phantom{;}\phantom{;}\\\end{array}$

$x+\frac{2}{3}+\frac{-x-\frac{19}{3}}{3x^2+2}$