$\begin{array}{l}\phantom{\phantom{;}j\phantom{;}-2;}{\phantom{;}j^{4}+2j^{3}+j^{2}+2j\phantom{;}+8\phantom{;}\phantom{;}}\\\phantom{;}j\phantom{;}-2\overline{\smash{)}\phantom{;}j^{5}\phantom{-;x^n}-3j^{3}\phantom{-;x^n}+4j\phantom{;}-6\phantom{;}\phantom{;}}\\\phantom{\phantom{;}j\phantom{;}-2;}\underline{-j^{5}+2j^{4}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-j^{5}+2j^{4};}\phantom{;}2j^{4}-3j^{3}\phantom{-;x^n}+4j\phantom{;}-6\phantom{;}\phantom{;}\\\phantom{\phantom{;}j\phantom{;}-2-;x^n;}\underline{-2j^{4}+4j^{3}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;-2j^{4}+4j^{3}-;x^n;}\phantom{;}j^{3}\phantom{-;x^n}+4j\phantom{;}-6\phantom{;}\phantom{;}\\\phantom{\phantom{;}j\phantom{;}-2-;x^n-;x^n;}\underline{-j^{3}+2j^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;;-j^{3}+2j^{2}-;x^n-;x^n;}\phantom{;}2j^{2}+4j\phantom{;}-6\phantom{;}\phantom{;}\\\phantom{\phantom{;}j\phantom{;}-2-;x^n-;x^n-;x^n;}\underline{-2j^{2}+4j\phantom{;}\phantom{-;x^n}}\\\phantom{;;;-2j^{2}+4j\phantom{;}-;x^n-;x^n-;x^n;}\phantom{;}8j\phantom{;}-6\phantom{;}\phantom{;}\\\phantom{\phantom{;}j\phantom{;}-2-;x^n-;x^n-;x^n-;x^n;}\underline{-8j\phantom{;}+16\phantom{;}\phantom{;}}\\\phantom{;;;;-8j\phantom{;}+16\phantom{;}\phantom{;}-;x^n-;x^n-;x^n-;x^n;}\phantom{;}10\phantom{;}\phantom{;}\\\end{array}$

$j^{4}+2j^{3}+j^{2}+2j+8+\frac{10}{j-2}$