$\begin{array}{l}\phantom{\phantom{;}x\phantom{;}-4;}{\phantom{;}2x^{2}+13x\phantom{;}-5\phantom{;}\phantom{;}}\\\phantom{;}x\phantom{;}-4\overline{\smash{)}\phantom{;}2x^{3}+5x^{2}-57x\phantom{;}+6\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x\phantom{;}-4;}\underline{-2x^{3}+8x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-2x^{3}+8x^{2};}\phantom{;}13x^{2}-57x\phantom{;}+6\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}-4-;x^n;}\underline{-13x^{2}+52x\phantom{;}\phantom{-;x^n}}\\\phantom{;-13x^{2}+52x\phantom{;}-;x^n;}-5x\phantom{;}+6\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}-4-;x^n-;x^n;}\underline{\phantom{;}5x\phantom{;}-20\phantom{;}\phantom{;}}\\\phantom{;;\phantom{;}5x\phantom{;}-20\phantom{;}\phantom{;}-;x^n-;x^n;}-14\phantom{;}\phantom{;}\\\end{array}$

$2x^{2}+13x-5+\frac{-14}{x-4}$