$\begin{array}{l}\phantom{\phantom{;}x\phantom{;}-2;}{\phantom{;}6x^{3}+10x^{2}+20x\phantom{;}+42\phantom{;}\phantom{;}}\\\phantom{;}x\phantom{;}-2\overline{\smash{)}\phantom{;}6x^{4}-2x^{3}\phantom{-;x^n}+2x\phantom{;}-5\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x\phantom{;}-2;}\underline{-6x^{4}+12x^{3}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-6x^{4}+12x^{3};}\phantom{;}10x^{3}\phantom{-;x^n}+2x\phantom{;}-5\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}-2-;x^n;}\underline{-10x^{3}+20x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;-10x^{3}+20x^{2}-;x^n;}\phantom{;}20x^{2}+2x\phantom{;}-5\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}-2-;x^n-;x^n;}\underline{-20x^{2}+40x\phantom{;}\phantom{-;x^n}}\\\phantom{;;-20x^{2}+40x\phantom{;}-;x^n-;x^n;}\phantom{;}42x\phantom{;}-5\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}-2-;x^n-;x^n-;x^n;}\underline{-42x\phantom{;}+84\phantom{;}\phantom{;}}\\\phantom{;;;-42x\phantom{;}+84\phantom{;}\phantom{;}-;x^n-;x^n-;x^n;}\phantom{;}79\phantom{;}\phantom{;}\\\end{array}$

$6x^{3}+10x^{2}+20x+42+\frac{79}{x-2}$