$\begin{array}{l}\phantom{\phantom{;}x\phantom{;}+1;}{\phantom{;}20x^{4}-20x^{3}+18x^{2}-18x\phantom{;}+21\phantom{;}\phantom{;}}\\\phantom{;}x\phantom{;}+1\overline{\smash{)}\phantom{;}20x^{5}\phantom{-;x^n}-2x^{3}\phantom{-;x^n}+3x\phantom{;}-10\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x\phantom{;}+1;}\underline{-20x^{5}-20x^{4}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-20x^{5}-20x^{4};}-20x^{4}-2x^{3}\phantom{-;x^n}+3x\phantom{;}-10\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+1-;x^n;}\underline{\phantom{;}20x^{4}+20x^{3}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;\phantom{;}20x^{4}+20x^{3}-;x^n;}\phantom{;}18x^{3}\phantom{-;x^n}+3x\phantom{;}-10\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+1-;x^n-;x^n;}\underline{-18x^{3}-18x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;;-18x^{3}-18x^{2}-;x^n-;x^n;}-18x^{2}+3x\phantom{;}-10\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+1-;x^n-;x^n-;x^n;}\underline{\phantom{;}18x^{2}+18x\phantom{;}\phantom{-;x^n}}\\\phantom{;;;\phantom{;}18x^{2}+18x\phantom{;}-;x^n-;x^n-;x^n;}\phantom{;}21x\phantom{;}-10\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+1-;x^n-;x^n-;x^n-;x^n;}\underline{-21x\phantom{;}-21\phantom{;}\phantom{;}}\\\phantom{;;;;-21x\phantom{;}-21\phantom{;}\phantom{;}-;x^n-;x^n-;x^n-;x^n;}-31\phantom{;}\phantom{;}\\\end{array}$

$20x^{4}-20x^{3}+18x^{2}-18x+21+\frac{-31}{x+1}$