$\begin{array}{l}\phantom{\phantom{;}x\phantom{;}-2;}{\phantom{;}4x^{2}+5x\phantom{;}-5\phantom{;}\phantom{;}}\\\phantom{;}x\phantom{;}-2\overline{\smash{)}\phantom{;}4x^{3}-3x^{2}-15x\phantom{;}+13\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x\phantom{;}-2;}\underline{-4x^{3}+8x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-4x^{3}+8x^{2};}\phantom{;}5x^{2}-15x\phantom{;}+13\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}-2-;x^n;}\underline{-5x^{2}+10x\phantom{;}\phantom{-;x^n}}\\\phantom{;-5x^{2}+10x\phantom{;}-;x^n;}-5x\phantom{;}+13\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}-2-;x^n-;x^n;}\underline{\phantom{;}5x\phantom{;}-10\phantom{;}\phantom{;}}\\\phantom{;;\phantom{;}5x\phantom{;}-10\phantom{;}\phantom{;}-;x^n-;x^n;}\phantom{;}3\phantom{;}\phantom{;}\\\end{array}$

$4x^{2}+5x-5+\frac{3}{x-2}$