$\begin{array}{l}\phantom{\phantom{;}x\phantom{;}-2;}{\phantom{;}2x^{4}+4x^{3}+11x^{2}+19x\phantom{;}+39\phantom{;}\phantom{;}}\\\phantom{;}x\phantom{;}-2\overline{\smash{)}\phantom{;}2x^{5}\phantom{-;x^n}+3x^{3}-3x^{2}+x\phantom{;}-1\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x\phantom{;}-2;}\underline{-2x^{5}+4x^{4}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-2x^{5}+4x^{4};}\phantom{;}4x^{4}+3x^{3}-3x^{2}+x\phantom{;}-1\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}-2-;x^n;}\underline{-4x^{4}+8x^{3}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;-4x^{4}+8x^{3}-;x^n;}\phantom{;}11x^{3}-3x^{2}+x\phantom{;}-1\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}-2-;x^n-;x^n;}\underline{-11x^{3}+22x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;;-11x^{3}+22x^{2}-;x^n-;x^n;}\phantom{;}19x^{2}+x\phantom{;}-1\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}-2-;x^n-;x^n-;x^n;}\underline{-19x^{2}+38x\phantom{;}\phantom{-;x^n}}\\\phantom{;;;-19x^{2}+38x\phantom{;}-;x^n-;x^n-;x^n;}\phantom{;}39x\phantom{;}-1\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}-2-;x^n-;x^n-;x^n-;x^n;}\underline{-39x\phantom{;}+78\phantom{;}\phantom{;}}\\\phantom{;;;;-39x\phantom{;}+78\phantom{;}\phantom{;}-;x^n-;x^n-;x^n-;x^n;}\phantom{;}77\phantom{;}\phantom{;}\\\end{array}$

$2x^{4}+4x^{3}+11x^{2}+19x+39+\frac{77}{x-2}$