$\begin{array}{l}\phantom{\phantom{;}x\phantom{;}+3;}{\phantom{;}3x^{3}-9x^{2}-8x\phantom{;}+15\phantom{;}\phantom{;}}\\\phantom{;}x\phantom{;}+3\overline{\smash{)}\phantom{;}3x^{4}\phantom{-;x^n}-35x^{2}-9x\phantom{;}+4\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x\phantom{;}+3;}\underline{-3x^{4}-9x^{3}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-3x^{4}-9x^{3};}-9x^{3}-35x^{2}-9x\phantom{;}+4\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+3-;x^n;}\underline{\phantom{;}9x^{3}+27x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;\phantom{;}9x^{3}+27x^{2}-;x^n;}-8x^{2}-9x\phantom{;}+4\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+3-;x^n-;x^n;}\underline{\phantom{;}8x^{2}+24x\phantom{;}\phantom{-;x^n}}\\\phantom{;;\phantom{;}8x^{2}+24x\phantom{;}-;x^n-;x^n;}\phantom{;}15x\phantom{;}+4\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+3-;x^n-;x^n-;x^n;}\underline{-15x\phantom{;}-45\phantom{;}\phantom{;}}\\\phantom{;;;-15x\phantom{;}-45\phantom{;}\phantom{;}-;x^n-;x^n-;x^n;}-41\phantom{;}\phantom{;}\\\end{array}$

$3x^{3}-9x^{2}-8x+15+\frac{-41}{x+3}$