$\begin{array}{l}\phantom{\phantom{;}x\phantom{;}+3;}{\phantom{;}5x^{3}-15x^{2}+39x\phantom{;}-114\phantom{;}\phantom{;}}\\\phantom{;}x\phantom{;}+3\overline{\smash{)}\phantom{;}5x^{4}\phantom{-;x^n}-6x^{2}+3x\phantom{;}-6\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x\phantom{;}+3;}\underline{-5x^{4}-15x^{3}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-5x^{4}-15x^{3};}-15x^{3}-6x^{2}+3x\phantom{;}-6\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+3-;x^n;}\underline{\phantom{;}15x^{3}+45x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;\phantom{;}15x^{3}+45x^{2}-;x^n;}\phantom{;}39x^{2}+3x\phantom{;}-6\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+3-;x^n-;x^n;}\underline{-39x^{2}-117x\phantom{;}\phantom{-;x^n}}\\\phantom{;;-39x^{2}-117x\phantom{;}-;x^n-;x^n;}-114x\phantom{;}-6\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+3-;x^n-;x^n-;x^n;}\underline{\phantom{;}114x\phantom{;}+342\phantom{;}\phantom{;}}\\\phantom{;;;\phantom{;}114x\phantom{;}+342\phantom{;}\phantom{;}-;x^n-;x^n-;x^n;}\phantom{;}336\phantom{;}\phantom{;}\\\end{array}$

$5x^{3}-15x^{2}+39x-114+\frac{336}{x+3}$