$\begin{array}{l}\phantom{\phantom{;}x\phantom{;}+2;}{\phantom{;}x^{3}-5x^{2}+13x\phantom{;}-23\phantom{;}\phantom{;}}\\\phantom{;}x\phantom{;}+2\overline{\smash{)}\phantom{;}x^{4}-3x^{3}+3x^{2}+3x\phantom{;}+2\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x\phantom{;}+2;}\underline{-x^{4}-2x^{3}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-x^{4}-2x^{3};}-5x^{3}+3x^{2}+3x\phantom{;}+2\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+2-;x^n;}\underline{\phantom{;}5x^{3}+10x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;\phantom{;}5x^{3}+10x^{2}-;x^n;}\phantom{;}13x^{2}+3x\phantom{;}+2\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+2-;x^n-;x^n;}\underline{-13x^{2}-26x\phantom{;}\phantom{-;x^n}}\\\phantom{;;-13x^{2}-26x\phantom{;}-;x^n-;x^n;}-23x\phantom{;}+2\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+2-;x^n-;x^n-;x^n;}\underline{\phantom{;}23x\phantom{;}+46\phantom{;}\phantom{;}}\\\phantom{;;;\phantom{;}23x\phantom{;}+46\phantom{;}\phantom{;}-;x^n-;x^n-;x^n;}\phantom{;}48\phantom{;}\phantom{;}\\\end{array}$

$x^{3}-5x^{2}+13x-23+\frac{48}{x+2}$