$\begin{array}{l}\phantom{\phantom{;}x\phantom{;}-2;}{\phantom{;}x^{4}+5x^{3}+10x^{2}+20x\phantom{;}+42\phantom{;}\phantom{;}}\\\phantom{;}x\phantom{;}-2\overline{\smash{)}\phantom{;}x^{5}+3x^{4}\phantom{-;x^n}\phantom{-;x^n}+2x\phantom{;}-1\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x\phantom{;}-2;}\underline{-x^{5}+2x^{4}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-x^{5}+2x^{4};}\phantom{;}5x^{4}\phantom{-;x^n}\phantom{-;x^n}+2x\phantom{;}-1\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}-2-;x^n;}\underline{-5x^{4}+10x^{3}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;-5x^{4}+10x^{3}-;x^n;}\phantom{;}10x^{3}\phantom{-;x^n}+2x\phantom{;}-1\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}-2-;x^n-;x^n;}\underline{-10x^{3}+20x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;;-10x^{3}+20x^{2}-;x^n-;x^n;}\phantom{;}20x^{2}+2x\phantom{;}-1\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}-2-;x^n-;x^n-;x^n;}\underline{-20x^{2}+40x\phantom{;}\phantom{-;x^n}}\\\phantom{;;;-20x^{2}+40x\phantom{;}-;x^n-;x^n-;x^n;}\phantom{;}42x\phantom{;}-1\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}-2-;x^n-;x^n-;x^n-;x^n;}\underline{-42x\phantom{;}+84\phantom{;}\phantom{;}}\\\phantom{;;;;-42x\phantom{;}+84\phantom{;}\phantom{;}-;x^n-;x^n-;x^n-;x^n;}\phantom{;}83\phantom{;}\phantom{;}\\\end{array}$

$x^{4}+5x^{3}+10x^{2}+20x+42+\frac{83}{x-2}$