$\begin{array}{l}\phantom{\phantom{;}x^{2}-4x\phantom{;}-1;}{\phantom{;}x^{2}+x\phantom{;}+2\phantom{;}\phantom{;}}\\\phantom{;}x^{2}-4x\phantom{;}-1\overline{\smash{)}\phantom{;}x^{4}-3x^{3}-3x^{2}+5x\phantom{;}+1\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x^{2}-4x\phantom{;}-1;}\underline{-x^{4}+4x^{3}+x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-x^{4}+4x^{3}+x^{2};}\phantom{;}x^{3}-2x^{2}+5x\phantom{;}+1\phantom{;}\phantom{;}\\\phantom{\phantom{;}x^{2}-4x\phantom{;}-1-;x^n;}\underline{-x^{3}+4x^{2}+x\phantom{;}\phantom{-;x^n}}\\\phantom{;-x^{3}+4x^{2}+x\phantom{;}-;x^n;}\phantom{;}2x^{2}+6x\phantom{;}+1\phantom{;}\phantom{;}\\\phantom{\phantom{;}x^{2}-4x\phantom{;}-1-;x^n-;x^n;}\underline{-2x^{2}+8x\phantom{;}+2\phantom{;}\phantom{;}}\\\phantom{;;-2x^{2}+8x\phantom{;}+2\phantom{;}\phantom{;}-;x^n-;x^n;}\phantom{;}14x\phantom{;}+3\phantom{;}\phantom{;}\\\end{array}$

$x^{2}+x+2+\frac{14x+3}{x^2-4x-1}$