a:
ĐKXĐ: \(\left\{{}\begin{matrix}x>=0\\x\ne4\end{matrix}\right.\)
\(M=\left(\dfrac{\sqrt{x}}{\sqrt{x}-2}+\dfrac{1}{\sqrt{x}+2}-\dfrac{2}{4-x}\right):\dfrac{\sqrt{x}+3}{\sqrt{x}-2}\)
\(=\left(\dfrac{\sqrt{x}}{\sqrt{x}-2}+\dfrac{1}{\sqrt{x}+2}+\dfrac{2}{\left(\sqrt{x}-2\right)\left(\sqrt{x}+2\right)}\right)\cdot\dfrac{\sqrt{x}-2}{\sqrt{x}+3}\)
\(=\dfrac{\sqrt{x}\left(\sqrt{x}+2\right)+\sqrt{x}-2+2}{\left(\sqrt{x}-2\right)\left(\sqrt{x}+2\right)}\cdot\dfrac{\sqrt{x}-2}{\sqrt{x}+3}\)
\(=\dfrac{x+3\sqrt{x}}{\left(\sqrt{x}+3\right)\left(\sqrt{x}+2\right)}=\dfrac{\sqrt{x}}{\sqrt{x}+2}\)
b: \(M-2=\dfrac{\sqrt{x}}{\sqrt{x}+2}-2=\dfrac{\sqrt{x}-2\sqrt{x}-4}{\sqrt{x}+2}=\dfrac{-\sqrt{x}-4}{\sqrt{x}+2}< 0\)
=>M<2
