$\begin{array}{l}\phantom{\phantom{;}x\phantom{;}-2;}{\phantom{;}x^{4}+2x^{3}+4x^{2}+7x\phantom{;}+17\phantom{;}\phantom{;}}\\\phantom{;}x\phantom{;}-2\overline{\smash{)}\phantom{;}x^{5}\phantom{-;x^n}\phantom{-;x^n}-x^{2}+3x\phantom{;}+2\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x\phantom{;}-2;}\underline{-x^{5}+2x^{4}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-x^{5}+2x^{4};}\phantom{;}2x^{4}\phantom{-;x^n}-x^{2}+3x\phantom{;}+2\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}-2-;x^n;}\underline{-2x^{4}+4x^{3}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;-2x^{4}+4x^{3}-;x^n;}\phantom{;}4x^{3}-x^{2}+3x\phantom{;}+2\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}-2-;x^n-;x^n;}\underline{-4x^{3}+8x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;;-4x^{3}+8x^{2}-;x^n-;x^n;}\phantom{;}7x^{2}+3x\phantom{;}+2\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}-2-;x^n-;x^n-;x^n;}\underline{-7x^{2}+14x\phantom{;}\phantom{-;x^n}}\\\phantom{;;;-7x^{2}+14x\phantom{;}-;x^n-;x^n-;x^n;}\phantom{;}17x\phantom{;}+2\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}-2-;x^n-;x^n-;x^n-;x^n;}\underline{-17x\phantom{;}+34\phantom{;}\phantom{;}}\\\phantom{;;;;-17x\phantom{;}+34\phantom{;}\phantom{;}-;x^n-;x^n-;x^n-;x^n;}\phantom{;}36\phantom{;}\phantom{;}\\\end{array}$

$x^{4}+2x^{3}+4x^{2}+7x+17+\frac{36}{x-2}$