$\begin{array}{l}\phantom{\phantom{;}x\phantom{;}+2;}{\phantom{;}3x^{3}-2x^{2}+2x\phantom{;}-4\phantom{;}\phantom{;}}\\\phantom{;}x\phantom{;}+2\overline{\smash{)}\phantom{;}3x^{4}+4x^{3}-2x^{2}\phantom{-;x^n}+1\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x\phantom{;}+2;}\underline{-3x^{4}-6x^{3}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-3x^{4}-6x^{3};}-2x^{3}-2x^{2}\phantom{-;x^n}+1\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+2-;x^n;}\underline{\phantom{;}2x^{3}+4x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;\phantom{;}2x^{3}+4x^{2}-;x^n;}\phantom{;}2x^{2}\phantom{-;x^n}+1\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+2-;x^n-;x^n;}\underline{-2x^{2}-4x\phantom{;}\phantom{-;x^n}}\\\phantom{;;-2x^{2}-4x\phantom{;}-;x^n-;x^n;}-4x\phantom{;}+1\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+2-;x^n-;x^n-;x^n;}\underline{\phantom{;}4x\phantom{;}+8\phantom{;}\phantom{;}}\\\phantom{;;;\phantom{;}4x\phantom{;}+8\phantom{;}\phantom{;}-;x^n-;x^n-;x^n;}\phantom{;}9\phantom{;}\phantom{;}\\\end{array}$

$3x^{3}-2x^{2}+2x-4+\frac{9}{x+2}$