$\begin{array}{l}\phantom{\phantom{;}x\phantom{;}+3;}{\phantom{;}x^{2}-3x\phantom{;}+1\phantom{;}\phantom{;}}\\\phantom{;}x\phantom{;}+3\overline{\smash{)}\phantom{;}x^{3}\phantom{-;x^n}-8x\phantom{;}-5\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x\phantom{;}+3;}\underline{-x^{3}-3x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-x^{3}-3x^{2};}-3x^{2}-8x\phantom{;}-5\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+3-;x^n;}\underline{\phantom{;}3x^{2}+9x\phantom{;}\phantom{-;x^n}}\\\phantom{;\phantom{;}3x^{2}+9x\phantom{;}-;x^n;}\phantom{;}x\phantom{;}-5\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+3-;x^n-;x^n;}\underline{-x\phantom{;}-3\phantom{;}\phantom{;}}\\\phantom{;;-x\phantom{;}-3\phantom{;}\phantom{;}-;x^n-;x^n;}-8\phantom{;}\phantom{;}\\\end{array}$

$x^{2}-3x+1+\frac{-8}{x+3}$