$\begin{array}{l}\phantom{\phantom{;}x\phantom{;}+3;}{\phantom{;}3x^{3}-9x^{2}+59x\phantom{;}-177\phantom{;}\phantom{;}}\\\phantom{;}x\phantom{;}+3\overline{\smash{)}\phantom{;}3x^{4}\phantom{-;x^n}+32x^{2}\phantom{-;x^n}+45\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x\phantom{;}+3;}\underline{-3x^{4}-9x^{3}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-3x^{4}-9x^{3};}-9x^{3}+32x^{2}\phantom{-;x^n}+45\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+3-;x^n;}\underline{\phantom{;}9x^{3}+27x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;\phantom{;}9x^{3}+27x^{2}-;x^n;}\phantom{;}59x^{2}\phantom{-;x^n}+45\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+3-;x^n-;x^n;}\underline{-59x^{2}-177x\phantom{;}\phantom{-;x^n}}\\\phantom{;;-59x^{2}-177x\phantom{;}-;x^n-;x^n;}-177x\phantom{;}+45\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+3-;x^n-;x^n-;x^n;}\underline{\phantom{;}177x\phantom{;}+531\phantom{;}\phantom{;}}\\\phantom{;;;\phantom{;}177x\phantom{;}+531\phantom{;}\phantom{;}-;x^n-;x^n-;x^n;}\phantom{;}576\phantom{;}\phantom{;}\\\end{array}$

$3x^{3}-9x^{2}+59x-177+\frac{576}{x+3}$