$\begin{array}{l}\phantom{\phantom{;}x\phantom{;}-7;}{\phantom{;}x^{3}-5x^{2}+6x\phantom{;}+24\phantom{;}\phantom{;}}\\\phantom{;}x\phantom{;}-7\overline{\smash{)}\phantom{;}x^{4}-12x^{3}+41x^{2}-18x\phantom{;}-72\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x\phantom{;}-7;}\underline{-x^{4}+7x^{3}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-x^{4}+7x^{3};}-5x^{3}+41x^{2}-18x\phantom{;}-72\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}-7-;x^n;}\underline{\phantom{;}5x^{3}-35x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;\phantom{;}5x^{3}-35x^{2}-;x^n;}\phantom{;}6x^{2}-18x\phantom{;}-72\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}-7-;x^n-;x^n;}\underline{-6x^{2}+42x\phantom{;}\phantom{-;x^n}}\\\phantom{;;-6x^{2}+42x\phantom{;}-;x^n-;x^n;}\phantom{;}24x\phantom{;}-72\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}-7-;x^n-;x^n-;x^n;}\underline{-24x\phantom{;}+168\phantom{;}\phantom{;}}\\\phantom{;;;-24x\phantom{;}+168\phantom{;}\phantom{;}-;x^n-;x^n-;x^n;}\phantom{;}96\phantom{;}\phantom{;}\\\end{array}$

$x^{3}-5x^{2}+6x+24+\frac{96}{x-7}$