$\begin{array}{l}\phantom{\phantom{;}x\phantom{;}+2;}{\phantom{;}2x^{4}-7x^{3}+17x^{2}-39x\phantom{;}+81\phantom{;}\phantom{;}}\\\phantom{;}x\phantom{;}+2\overline{\smash{)}\phantom{;}2x^{5}-3x^{4}+3x^{3}-5x^{2}+3x\phantom{;}+1\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x\phantom{;}+2;}\underline{-2x^{5}-4x^{4}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-2x^{5}-4x^{4};}-7x^{4}+3x^{3}-5x^{2}+3x\phantom{;}+1\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+2-;x^n;}\underline{\phantom{;}7x^{4}+14x^{3}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;\phantom{;}7x^{4}+14x^{3}-;x^n;}\phantom{;}17x^{3}-5x^{2}+3x\phantom{;}+1\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+2-;x^n-;x^n;}\underline{-17x^{3}-34x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;;-17x^{3}-34x^{2}-;x^n-;x^n;}-39x^{2}+3x\phantom{;}+1\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+2-;x^n-;x^n-;x^n;}\underline{\phantom{;}39x^{2}+78x\phantom{;}\phantom{-;x^n}}\\\phantom{;;;\phantom{;}39x^{2}+78x\phantom{;}-;x^n-;x^n-;x^n;}\phantom{;}81x\phantom{;}+1\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+2-;x^n-;x^n-;x^n-;x^n;}\underline{-81x\phantom{;}-162\phantom{;}\phantom{;}}\\\phantom{;;;;-81x\phantom{;}-162\phantom{;}\phantom{;}-;x^n-;x^n-;x^n-;x^n;}-161\phantom{;}\phantom{;}\\\end{array}$

$2x^{4}-7x^{3}+17x^{2}-39x+81+\frac{-161}{x+2}$