Final answer to the problem
$x+2+\frac{6}{x-2}$
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1
Divide $x^2+2$ by $x-2$
$\begin{array}{l}\phantom{\phantom{;}x\phantom{;}-2;}{\phantom{;}x\phantom{;}+2\phantom{;}\phantom{;}}\\\phantom{;}x\phantom{;}-2\overline{\smash{)}\phantom{;}x^{2}\phantom{-;x^n}+2\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x\phantom{;}-2;}\underline{-x^{2}+2x\phantom{;}\phantom{-;x^n}}\\\phantom{-x^{2}+2x\phantom{;};}\phantom{;}2x\phantom{;}+2\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}-2-;x^n;}\underline{-2x\phantom{;}+4\phantom{;}\phantom{;}}\\\phantom{;-2x\phantom{;}+4\phantom{;}\phantom{;}-;x^n;}\phantom{;}6\phantom{;}\phantom{;}\\\end{array}$
2
Resulting polynomial
$x+2+\frac{6}{x-2}$
Final answer to the problem
$x+2+\frac{6}{x-2}$
