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