a: ĐKXĐ: \(\left\{{}\begin{matrix}x>=0\\x\ne4\end{matrix}\right.\)
\(A=\left(\dfrac{\sqrt{x}}{x-4}-\dfrac{1}{2-\sqrt{x}}\right):\dfrac{2}{\sqrt{x}-2}\)
\(=\left(\dfrac{\sqrt{x}}{\left(\sqrt{x}-2\right)\cdot\left(\sqrt{x}+2\right)}+\dfrac{1}{\sqrt{x}-2}\right)\cdot\dfrac{\sqrt{x}-2}{2}\)
\(=\dfrac{\sqrt{x}+\sqrt{x}+2}{\left(\sqrt{x}-2\right)\left(\sqrt{x}+2\right)}\cdot\dfrac{\sqrt{x}-2}{2}\)
\(=\dfrac{2\left(\sqrt{x}+1\right)}{2\left(\sqrt{x}+2\right)}=\dfrac{\sqrt{x}+1}{\sqrt{x}+2}\)
b: \(A^2-A=A\left(A-1\right)=\dfrac{\sqrt{x}+1}{\sqrt{x}+2}\cdot\left(\dfrac{\sqrt{x}+1}{\sqrt{x}+2}-1\right)\)
\(=\dfrac{\sqrt{x}+1}{\sqrt{x}+2}\cdot\dfrac{-1}{\sqrt{x}+2}=\dfrac{-\left(\sqrt{x}+1\right)}{\left(\sqrt{x}+2\right)^2}< 0\)
=>\(A^2< A\)