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

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