$\begin{array}{l}\phantom{\phantom{;}x\phantom{;}-2;}{\phantom{;}x^{3}+2x^{2}+5x\phantom{;}+7\phantom{;}\phantom{;}}\\\phantom{;}x\phantom{;}-2\overline{\smash{)}\phantom{;}x^{4}\phantom{-;x^n}+x^{2}-3x\phantom{;}+2\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x\phantom{;}-2;}\underline{-x^{4}+2x^{3}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-x^{4}+2x^{3};}\phantom{;}2x^{3}+x^{2}-3x\phantom{;}+2\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}-2-;x^n;}\underline{-2x^{3}+4x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;-2x^{3}+4x^{2}-;x^n;}\phantom{;}5x^{2}-3x\phantom{;}+2\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}-2-;x^n-;x^n;}\underline{-5x^{2}+10x\phantom{;}\phantom{-;x^n}}\\\phantom{;;-5x^{2}+10x\phantom{;}-;x^n-;x^n;}\phantom{;}7x\phantom{;}+2\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}-2-;x^n-;x^n-;x^n;}\underline{-7x\phantom{;}+14\phantom{;}\phantom{;}}\\\phantom{;;;-7x\phantom{;}+14\phantom{;}\phantom{;}-;x^n-;x^n-;x^n;}\phantom{;}16\phantom{;}\phantom{;}\\\end{array}$

$x^{3}+2x^{2}+5x+7+\frac{16}{x-2}$