$\begin{array}{l}\phantom{\phantom{;}x\phantom{;}+3;}{-x^{3}+3x^{2}+x\phantom{;}-1\phantom{;}\phantom{;}}\\\phantom{;}x\phantom{;}+3\overline{\smash{)}-x^{4}\phantom{-;x^n}+10x^{2}+2x\phantom{;}-2\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x\phantom{;}+3;}\underline{\phantom{;}x^{4}+3x^{3}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{\phantom{;}x^{4}+3x^{3};}\phantom{;}3x^{3}+10x^{2}+2x\phantom{;}-2\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+3-;x^n;}\underline{-3x^{3}-9x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;-3x^{3}-9x^{2}-;x^n;}\phantom{;}x^{2}+2x\phantom{;}-2\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+3-;x^n-;x^n;}\underline{-x^{2}-3x\phantom{;}\phantom{-;x^n}}\\\phantom{;;-x^{2}-3x\phantom{;}-;x^n-;x^n;}-x\phantom{;}-2\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+3-;x^n-;x^n-;x^n;}\underline{\phantom{;}x\phantom{;}+3\phantom{;}\phantom{;}}\\\phantom{;;;\phantom{;}x\phantom{;}+3\phantom{;}\phantom{;}-;x^n-;x^n-;x^n;}\phantom{;}1\phantom{;}\phantom{;}\\\end{array}$

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