$\begin{array}{l}\phantom{\phantom{;}x\phantom{;}-2;}{\phantom{;}x^{3}+2x^{2}+7x\phantom{;}+13\phantom{;}\phantom{;}}\\\phantom{;}x\phantom{;}-2\overline{\smash{)}\phantom{;}x^{4}\phantom{-;x^n}+3x^{2}-x\phantom{;}-3\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x\phantom{;}-2;}\underline{-x^{4}+2x^{3}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-x^{4}+2x^{3};}\phantom{;}2x^{3}+3x^{2}-x\phantom{;}-3\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}-2-;x^n;}\underline{-2x^{3}+4x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;-2x^{3}+4x^{2}-;x^n;}\phantom{;}7x^{2}-x\phantom{;}-3\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}-2-;x^n-;x^n;}\underline{-7x^{2}+14x\phantom{;}\phantom{-;x^n}}\\\phantom{;;-7x^{2}+14x\phantom{;}-;x^n-;x^n;}\phantom{;}13x\phantom{;}-3\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}-2-;x^n-;x^n-;x^n;}\underline{-13x\phantom{;}+26\phantom{;}\phantom{;}}\\\phantom{;;;-13x\phantom{;}+26\phantom{;}\phantom{;}-;x^n-;x^n-;x^n;}\phantom{;}23\phantom{;}\phantom{;}\\\end{array}$

$x^{3}+2x^{2}+7x+13+\frac{23}{x-2}$