$\begin{array}{l}\phantom{\phantom{;}x\phantom{;}-2;}{\phantom{;}x^{3}+2x^{2}+4x\phantom{;}+6\phantom{;}\phantom{;}}\\\phantom{;}x\phantom{;}-2\overline{\smash{)}\phantom{;}x^{4}\phantom{-;x^n}\phantom{-;x^n}-2x\phantom{;}+3\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x\phantom{;}-2;}\underline{-x^{4}+2x^{3}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-x^{4}+2x^{3};}\phantom{;}2x^{3}\phantom{-;x^n}-2x\phantom{;}+3\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}-2-;x^n;}\underline{-2x^{3}+4x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;-2x^{3}+4x^{2}-;x^n;}\phantom{;}4x^{2}-2x\phantom{;}+3\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}-2-;x^n-;x^n;}\underline{-4x^{2}+8x\phantom{;}\phantom{-;x^n}}\\\phantom{;;-4x^{2}+8x\phantom{;}-;x^n-;x^n;}\phantom{;}6x\phantom{;}+3\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}-2-;x^n-;x^n-;x^n;}\underline{-6x\phantom{;}+12\phantom{;}\phantom{;}}\\\phantom{;;;-6x\phantom{;}+12\phantom{;}\phantom{;}-;x^n-;x^n-;x^n;}\phantom{;}15\phantom{;}\phantom{;}\\\end{array}$

$x^{3}+2x^{2}+4x+6+\frac{15}{x-2}$