$\begin{array}{l}\phantom{\phantom{;}x\phantom{;}+3;}{\phantom{;}x^{3}-4x^{2}+12x\phantom{;}-38\phantom{;}\phantom{;}}\\\phantom{;}x\phantom{;}+3\overline{\smash{)}\phantom{;}x^{4}-x^{3}\phantom{-;x^n}-2x\phantom{;}-8\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x\phantom{;}+3;}\underline{-x^{4}-3x^{3}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-x^{4}-3x^{3};}-4x^{3}\phantom{-;x^n}-2x\phantom{;}-8\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+3-;x^n;}\underline{\phantom{;}4x^{3}+12x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;\phantom{;}4x^{3}+12x^{2}-;x^n;}\phantom{;}12x^{2}-2x\phantom{;}-8\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+3-;x^n-;x^n;}\underline{-12x^{2}-36x\phantom{;}\phantom{-;x^n}}\\\phantom{;;-12x^{2}-36x\phantom{;}-;x^n-;x^n;}-38x\phantom{;}-8\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+3-;x^n-;x^n-;x^n;}\underline{\phantom{;}38x\phantom{;}+114\phantom{;}\phantom{;}}\\\phantom{;;;\phantom{;}38x\phantom{;}+114\phantom{;}\phantom{;}-;x^n-;x^n-;x^n;}\phantom{;}106\phantom{;}\phantom{;}\\\end{array}$

$x^{3}-4x^{2}+12x-38+\frac{106}{x+3}$