$\begin{array}{l}\phantom{\phantom{;}x\phantom{;}-2;}{\phantom{;}4x^{3}+11x^{2}+22x\phantom{;}+42\phantom{;}\phantom{;}}\\\phantom{;}x\phantom{;}-2\overline{\smash{)}\phantom{;}4x^{4}+3x^{3}\phantom{-;x^n}-2x\phantom{;}+1\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x\phantom{;}-2;}\underline{-4x^{4}+8x^{3}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-4x^{4}+8x^{3};}\phantom{;}11x^{3}\phantom{-;x^n}-2x\phantom{;}+1\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}-2-;x^n;}\underline{-11x^{3}+22x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;-11x^{3}+22x^{2}-;x^n;}\phantom{;}22x^{2}-2x\phantom{;}+1\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}-2-;x^n-;x^n;}\underline{-22x^{2}+44x\phantom{;}\phantom{-;x^n}}\\\phantom{;;-22x^{2}+44x\phantom{;}-;x^n-;x^n;}\phantom{;}42x\phantom{;}+1\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}-2-;x^n-;x^n-;x^n;}\underline{-42x\phantom{;}+84\phantom{;}\phantom{;}}\\\phantom{;;;-42x\phantom{;}+84\phantom{;}\phantom{;}-;x^n-;x^n-;x^n;}\phantom{;}85\phantom{;}\phantom{;}\\\end{array}$

$4x^{3}+11x^{2}+22x+42+\frac{85}{x-2}$