$\begin{array}{l}\phantom{\phantom{;}y\phantom{;}-2;}{\phantom{;}y^{4}+2y^{3}+2y^{2}+4y\phantom{;}+10\phantom{;}\phantom{;}}\\\phantom{;}y\phantom{;}-2\overline{\smash{)}\phantom{;}y^{5}\phantom{-;x^n}-2y^{3}\phantom{-;x^n}+2y\phantom{;}-4\phantom{;}\phantom{;}}\\\phantom{\phantom{;}y\phantom{;}-2;}\underline{-y^{5}+2y^{4}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-y^{5}+2y^{4};}\phantom{;}2y^{4}-2y^{3}\phantom{-;x^n}+2y\phantom{;}-4\phantom{;}\phantom{;}\\\phantom{\phantom{;}y\phantom{;}-2-;x^n;}\underline{-2y^{4}+4y^{3}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;-2y^{4}+4y^{3}-;x^n;}\phantom{;}2y^{3}\phantom{-;x^n}+2y\phantom{;}-4\phantom{;}\phantom{;}\\\phantom{\phantom{;}y\phantom{;}-2-;x^n-;x^n;}\underline{-2y^{3}+4y^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;;-2y^{3}+4y^{2}-;x^n-;x^n;}\phantom{;}4y^{2}+2y\phantom{;}-4\phantom{;}\phantom{;}\\\phantom{\phantom{;}y\phantom{;}-2-;x^n-;x^n-;x^n;}\underline{-4y^{2}+8y\phantom{;}\phantom{-;x^n}}\\\phantom{;;;-4y^{2}+8y\phantom{;}-;x^n-;x^n-;x^n;}\phantom{;}10y\phantom{;}-4\phantom{;}\phantom{;}\\\phantom{\phantom{;}y\phantom{;}-2-;x^n-;x^n-;x^n-;x^n;}\underline{-10y\phantom{;}+20\phantom{;}\phantom{;}}\\\phantom{;;;;-10y\phantom{;}+20\phantom{;}\phantom{;}-;x^n-;x^n-;x^n-;x^n;}\phantom{;}16\phantom{;}\phantom{;}\\\end{array}$

$y^{4}+2y^{3}+2y^{2}+4y+10+\frac{16}{y-2}$