$\begin{array}{l}\phantom{\phantom{;}x^{2}-2x\phantom{;}+5;}{\phantom{;}x^{3}+2x^{2}-x\phantom{;}-12\phantom{;}\phantom{;}}\\\phantom{;}x^{2}-2x\phantom{;}+5\overline{\smash{)}\phantom{;}x^{5}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}+7x\phantom{;}-1\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x^{2}-2x\phantom{;}+5;}\underline{-x^{5}+2x^{4}-5x^{3}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-x^{5}+2x^{4}-5x^{3};}\phantom{;}2x^{4}-5x^{3}\phantom{-;x^n}+7x\phantom{;}-1\phantom{;}\phantom{;}\\\phantom{\phantom{;}x^{2}-2x\phantom{;}+5-;x^n;}\underline{-2x^{4}+4x^{3}-10x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;-2x^{4}+4x^{3}-10x^{2}-;x^n;}-x^{3}-10x^{2}+7x\phantom{;}-1\phantom{;}\phantom{;}\\\phantom{\phantom{;}x^{2}-2x\phantom{;}+5-;x^n-;x^n;}\underline{\phantom{;}x^{3}-2x^{2}+5x\phantom{;}\phantom{-;x^n}}\\\phantom{;;\phantom{;}x^{3}-2x^{2}+5x\phantom{;}-;x^n-;x^n;}-12x^{2}+12x\phantom{;}-1\phantom{;}\phantom{;}\\\phantom{\phantom{;}x^{2}-2x\phantom{;}+5-;x^n-;x^n-;x^n;}\underline{\phantom{;}12x^{2}-24x\phantom{;}+60\phantom{;}\phantom{;}}\\\phantom{;;;\phantom{;}12x^{2}-24x\phantom{;}+60\phantom{;}\phantom{;}-;x^n-;x^n-;x^n;}-12x\phantom{;}+59\phantom{;}\phantom{;}\\\end{array}$

$x^{3}+2x^{2}-x-12+\frac{-12x+59}{x^2-2x+5}$