$\begin{array}{l}\phantom{\phantom{;}x\phantom{;}-2;}{\phantom{;}3x^{3}+4x^{2}-2x\phantom{;}-4\phantom{;}\phantom{;}}\\\phantom{;}x\phantom{;}-2\overline{\smash{)}\phantom{;}3x^{4}-2x^{3}-10x^{2}\phantom{-;x^n}+15\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x\phantom{;}-2;}\underline{-3x^{4}+6x^{3}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-3x^{4}+6x^{3};}\phantom{;}4x^{3}-10x^{2}\phantom{-;x^n}+15\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}-2-;x^n;}\underline{-4x^{3}+8x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;-4x^{3}+8x^{2}-;x^n;}-2x^{2}\phantom{-;x^n}+15\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}-2-;x^n-;x^n;}\underline{\phantom{;}2x^{2}-4x\phantom{;}\phantom{-;x^n}}\\\phantom{;;\phantom{;}2x^{2}-4x\phantom{;}-;x^n-;x^n;}-4x\phantom{;}+15\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}-2-;x^n-;x^n-;x^n;}\underline{\phantom{;}4x\phantom{;}-8\phantom{;}\phantom{;}}\\\phantom{;;;\phantom{;}4x\phantom{;}-8\phantom{;}\phantom{;}-;x^n-;x^n-;x^n;}\phantom{;}7\phantom{;}\phantom{;}\\\end{array}$

$3x^{3}+4x^{2}-2x-4+\frac{7}{x-2}$