$\begin{array}{l}\phantom{\phantom{;}x^{2}+3;}{\phantom{;}3x\phantom{;}-2\phantom{;}\phantom{;}}\\\phantom{;}x^{2}+3\overline{\smash{)}\phantom{;}3x^{3}-2x^{2}+x\phantom{;}-4\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x^{2}+3;}\underline{-3x^{3}\phantom{-;x^n}-9x\phantom{;}\phantom{-;x^n}}\\\phantom{-3x^{3}-9x\phantom{;};}-2x^{2}-8x\phantom{;}-4\phantom{;}\phantom{;}\\\phantom{\phantom{;}x^{2}+3-;x^n;}\underline{\phantom{;}2x^{2}\phantom{-;x^n}+6\phantom{;}\phantom{;}}\\\phantom{;\phantom{;}2x^{2}+6\phantom{;}\phantom{;}-;x^n;}-8x\phantom{;}+2\phantom{;}\phantom{;}\\\end{array}$

$3x-2+\frac{-8x+2}{x^2+3}$