$\begin{array}{l}\phantom{\phantom{;}x\phantom{;}-2;}{\phantom{;}2x^{4}+6x^{3}+6x^{2}+13x\phantom{;}+25\phantom{;}\phantom{;}}\\\phantom{;}x\phantom{;}-2\overline{\smash{)}\phantom{;}2x^{5}+2x^{4}-6x^{3}+x^{2}-x\phantom{;}-2\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x\phantom{;}-2;}\underline{-2x^{5}+4x^{4}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-2x^{5}+4x^{4};}\phantom{;}6x^{4}-6x^{3}+x^{2}-x\phantom{;}-2\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}-2-;x^n;}\underline{-6x^{4}+12x^{3}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;-6x^{4}+12x^{3}-;x^n;}\phantom{;}6x^{3}+x^{2}-x\phantom{;}-2\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}-2-;x^n-;x^n;}\underline{-6x^{3}+12x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;;-6x^{3}+12x^{2}-;x^n-;x^n;}\phantom{;}13x^{2}-x\phantom{;}-2\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}-2-;x^n-;x^n-;x^n;}\underline{-13x^{2}+26x\phantom{;}\phantom{-;x^n}}\\\phantom{;;;-13x^{2}+26x\phantom{;}-;x^n-;x^n-;x^n;}\phantom{;}25x\phantom{;}-2\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}-2-;x^n-;x^n-;x^n-;x^n;}\underline{-25x\phantom{;}+50\phantom{;}\phantom{;}}\\\phantom{;;;;-25x\phantom{;}+50\phantom{;}\phantom{;}-;x^n-;x^n-;x^n-;x^n;}\phantom{;}48\phantom{;}\phantom{;}\\\end{array}$

$2x^{4}+6x^{3}+6x^{2}+13x+25+\frac{48}{x-2}$