\(2,\\ a,A=\dfrac{x-2x-4+x-2}{\left(x-2\right)\left(x+2\right)}:\dfrac{x^2-4+10-x^2}{x+2}\left(x\ne2\right)\\ A=\dfrac{-6}{\left(x+2\right)\left(x-2\right)}\cdot\dfrac{x+2}{-6}=\dfrac{1}{x-2}\\ b,\sqrt{x^2+x}=\sqrt{6}\\ \Leftrightarrow x^2+x-6=0\Leftrightarrow\left[{}\begin{matrix}x=-3\\x=2\end{matrix}\right.\\ \forall x=-3\Leftrightarrow A=\dfrac{1}{-5}=-\dfrac{1}{5}\\ \forall x=2\Leftrightarrow A\in\varnothing\left(ko.thỏa.mãn.ĐKXĐ\right)\)
\(c,A>0\Leftrightarrow\dfrac{1}{x-2}>0\Leftrightarrow x-2>0\left(1>0\right)\Leftrightarrow x>2\)
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