\(a,x=8\sqrt{3}-12+16-8\sqrt{3}=4\\ \Leftrightarrow E=\dfrac{2+1}{2}=\dfrac{3}{2}\\ b,A=EG=\dfrac{\sqrt{x}+1}{\sqrt{x}}\cdot\dfrac{\left(\sqrt{x}+2\right)\left(\sqrt{x}-1\right)-\left(\sqrt{x}-2\right)\left(\sqrt{x}+1\right)}{\left(\sqrt{x}+1\right)^2\left(\sqrt{x}-1\right)}\\ A=\dfrac{\sqrt{x}+1}{\sqrt{x}}\cdot\dfrac{x+\sqrt{x}-2-x+\sqrt{x}+2}{\left(\sqrt{x}+1\right)^2\left(\sqrt{x}-1\right)}\\ A=\dfrac{2\sqrt{x}}{\sqrt{x}\left(\sqrt{x}+1\right)\left(\sqrt{x}-1\right)}=\dfrac{2}{x-1}\)
\(c,\left|A+1\right|>A+1\\ \Leftrightarrow A+1< 0\\ \Leftrightarrow\dfrac{2+x-1}{x-1}< 0\\ \Leftrightarrow\dfrac{x+1}{x-1}< 0\Leftrightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}x+1>0\\x-1< 0\end{matrix}\right.\\\left\{{}\begin{matrix}x+1< 0\\x-1>0\end{matrix}\right.\end{matrix}\right.\Leftrightarrow-1< x< 1\)
