$\begin{array}{l}\phantom{\phantom{;}x\phantom{;}-2;}{\phantom{;}2x^{3}+5x^{2}+9x\phantom{;}+6\phantom{;}\phantom{;}}\\\phantom{;}x\phantom{;}-2\overline{\smash{)}\phantom{;}2x^{4}+x^{3}-x^{2}-12x\phantom{;}+1\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x\phantom{;}-2;}\underline{-2x^{4}+4x^{3}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-2x^{4}+4x^{3};}\phantom{;}5x^{3}-x^{2}-12x\phantom{;}+1\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}-2-;x^n;}\underline{-5x^{3}+10x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;-5x^{3}+10x^{2}-;x^n;}\phantom{;}9x^{2}-12x\phantom{;}+1\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}-2-;x^n-;x^n;}\underline{-9x^{2}+18x\phantom{;}\phantom{-;x^n}}\\\phantom{;;-9x^{2}+18x\phantom{;}-;x^n-;x^n;}\phantom{;}6x\phantom{;}+1\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}-2-;x^n-;x^n-;x^n;}\underline{-6x\phantom{;}+12\phantom{;}\phantom{;}}\\\phantom{;;;-6x\phantom{;}+12\phantom{;}\phantom{;}-;x^n-;x^n-;x^n;}\phantom{;}13\phantom{;}\phantom{;}\\\end{array}$

$2x^{3}+5x^{2}+9x+6+\frac{13}{x-2}$