$\begin{array}{l}\phantom{\phantom{;}x\phantom{;}+2;}{\phantom{;}x^{4}-2x^{3}\phantom{-;x^n}+2x\phantom{;}-5\phantom{;}\phantom{;}}\\\phantom{;}x\phantom{;}+2\overline{\smash{)}\phantom{;}x^{5}\phantom{-;x^n}-4x^{3}+2x^{2}-x\phantom{;}+7\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x\phantom{;}+2;}\underline{-x^{5}-2x^{4}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-x^{5}-2x^{4};}-2x^{4}-4x^{3}+2x^{2}-x\phantom{;}+7\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+2-;x^n;}\underline{\phantom{;}2x^{4}+4x^{3}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;\phantom{;}2x^{4}+4x^{3}-;x^n;}\phantom{;}2x^{2}-x\phantom{;}+7\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+2-;x^n-;x^n;}\underline{-2x^{2}-4x\phantom{;}\phantom{-;x^n}}\\\phantom{;;-2x^{2}-4x\phantom{;}-;x^n-;x^n;}-5x\phantom{;}+7\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+2-;x^n-;x^n-;x^n;}\underline{\phantom{;}5x\phantom{;}+10\phantom{;}\phantom{;}}\\\phantom{;;;\phantom{;}5x\phantom{;}+10\phantom{;}\phantom{;}-;x^n-;x^n-;x^n;}\phantom{;}17\phantom{;}\phantom{;}\\\end{array}$

$x^{4}-2x^{3}+2x-5+\frac{17}{x+2}$