$\begin{array}{l}\phantom{\phantom{;}x\phantom{;}+3;}{\phantom{;}3x^{3}-13x^{2}+39x\phantom{;}-112\phantom{;}\phantom{;}}\\\phantom{;}x\phantom{;}+3\overline{\smash{)}\phantom{;}3x^{4}-4x^{3}\phantom{-;x^n}+5x\phantom{;}-12\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x\phantom{;}+3;}\underline{-3x^{4}-9x^{3}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-3x^{4}-9x^{3};}-13x^{3}\phantom{-;x^n}+5x\phantom{;}-12\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+3-;x^n;}\underline{\phantom{;}13x^{3}+39x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;\phantom{;}13x^{3}+39x^{2}-;x^n;}\phantom{;}39x^{2}+5x\phantom{;}-12\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+3-;x^n-;x^n;}\underline{-39x^{2}-117x\phantom{;}\phantom{-;x^n}}\\\phantom{;;-39x^{2}-117x\phantom{;}-;x^n-;x^n;}-112x\phantom{;}-12\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+3-;x^n-;x^n-;x^n;}\underline{\phantom{;}112x\phantom{;}+336\phantom{;}\phantom{;}}\\\phantom{;;;\phantom{;}112x\phantom{;}+336\phantom{;}\phantom{;}-;x^n-;x^n-;x^n;}\phantom{;}324\phantom{;}\phantom{;}\\\end{array}$

$3x^{3}-13x^{2}+39x-112+\frac{324}{x+3}$