$\begin{array}{l}\phantom{\phantom{;}x\phantom{;}-2;}{\phantom{;}2x^{3}+3x^{2}+6x\phantom{;}+13\phantom{;}\phantom{;}}\\\phantom{;}x\phantom{;}-2\overline{\smash{)}\phantom{;}2x^{4}-x^{3}\phantom{-;x^n}+x\phantom{;}-1\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x\phantom{;}-2;}\underline{-2x^{4}+4x^{3}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-2x^{4}+4x^{3};}\phantom{;}3x^{3}\phantom{-;x^n}+x\phantom{;}-1\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}-2-;x^n;}\underline{-3x^{3}+6x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;-3x^{3}+6x^{2}-;x^n;}\phantom{;}6x^{2}+x\phantom{;}-1\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}-2-;x^n-;x^n;}\underline{-6x^{2}+12x\phantom{;}\phantom{-;x^n}}\\\phantom{;;-6x^{2}+12x\phantom{;}-;x^n-;x^n;}\phantom{;}13x\phantom{;}-1\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}-2-;x^n-;x^n-;x^n;}\underline{-13x\phantom{;}+26\phantom{;}\phantom{;}}\\\phantom{;;;-13x\phantom{;}+26\phantom{;}\phantom{;}-;x^n-;x^n-;x^n;}\phantom{;}25\phantom{;}\phantom{;}\\\end{array}$

$2x^{3}+3x^{2}+6x+13+\frac{25}{x-2}$