$\begin{array}{l}\phantom{\phantom{;}x\phantom{;}-2;}{\phantom{;}x^{4}+2x^{3}+4x^{2}+8x\phantom{;}+21\phantom{;}\phantom{;}}\\\phantom{;}x\phantom{;}-2\overline{\smash{)}\phantom{;}x^{5}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}+5x\phantom{;}+38\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x\phantom{;}-2;}\underline{-x^{5}+2x^{4}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-x^{5}+2x^{4};}\phantom{;}2x^{4}\phantom{-;x^n}\phantom{-;x^n}+5x\phantom{;}+38\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}-2-;x^n;}\underline{-2x^{4}+4x^{3}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;-2x^{4}+4x^{3}-;x^n;}\phantom{;}4x^{3}\phantom{-;x^n}+5x\phantom{;}+38\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}-2-;x^n-;x^n;}\underline{-4x^{3}+8x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;;-4x^{3}+8x^{2}-;x^n-;x^n;}\phantom{;}8x^{2}+5x\phantom{;}+38\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}-2-;x^n-;x^n-;x^n;}\underline{-8x^{2}+16x\phantom{;}\phantom{-;x^n}}\\\phantom{;;;-8x^{2}+16x\phantom{;}-;x^n-;x^n-;x^n;}\phantom{;}21x\phantom{;}+38\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}-2-;x^n-;x^n-;x^n-;x^n;}\underline{-21x\phantom{;}+42\phantom{;}\phantom{;}}\\\phantom{;;;;-21x\phantom{;}+42\phantom{;}\phantom{;}-;x^n-;x^n-;x^n-;x^n;}\phantom{;}80\phantom{;}\phantom{;}\\\end{array}$

$x^{4}+2x^{3}+4x^{2}+8x+21+\frac{80}{x-2}$