$\begin{array}{l}\phantom{\phantom{;}x\phantom{;}-2;}{\phantom{;}2x^{2}+4x\phantom{;}+5\phantom{;}\phantom{;}}\\\phantom{;}x\phantom{;}-2\overline{\smash{)}\phantom{;}2x^{3}\phantom{-;x^n}-3x\phantom{;}+8\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x\phantom{;}-2;}\underline{-2x^{3}+4x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-2x^{3}+4x^{2};}\phantom{;}4x^{2}-3x\phantom{;}+8\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}-2-;x^n;}\underline{-4x^{2}+8x\phantom{;}\phantom{-;x^n}}\\\phantom{;-4x^{2}+8x\phantom{;}-;x^n;}\phantom{;}5x\phantom{;}+8\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}-2-;x^n-;x^n;}\underline{-5x\phantom{;}+10\phantom{;}\phantom{;}}\\\phantom{;;-5x\phantom{;}+10\phantom{;}\phantom{;}-;x^n-;x^n;}\phantom{;}18\phantom{;}\phantom{;}\\\end{array}$

$2x^{2}+4x+5+\frac{18}{x-2}$