a, DKXD: \(\left\{{}\begin{matrix}x+2\ne0\\x-2\ne0\\x^2+4\ne0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x\ne-2\\x\ne2\end{matrix}\right.\)
b, \(C=\left(\dfrac{x}{x+2}+\dfrac{2}{x-2}\right).\dfrac{x^2+2x}{x^2+4}\)
\(=\dfrac{x\left(x-2\right)+2\left(x+2\right)}{x+2}.\dfrac{x\left(x+2\right)}{x^2+4}\)
\(=\dfrac{x^2-2x+2x+4}{x+2}.\dfrac{x\left(x+2\right)}{x^2+4}\)
\(=\dfrac{x^2+4}{x+2}.\dfrac{x\left(x+2\right)}{x^2+4}=x\)
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