a) $M$ có nghĩa ⇔ $\begin{cases} \sqrt x \text{ có nghĩa} \\ \sqrt{4x}\text{ có nghĩa}\\\sqrt x - 2 \neq 0 \\ \sqrt x + 2 \neq 0 \\\sqrt{4x} \neq 0\\\end{cases}$
⇔$\begin{cases} x \geq 0 \\ 4x \geq 0 \\ \sqrt x \neq 2 \\ \sqrt x \neq -2 \\ 4x \neq 0 \\\end{cases}$
⇔$\begin{cases} x \geq 0 \\ x \neq 4 \\ x \neq 0\\\end{cases}$
⇔$\begin{cases} x > 0 \\ x \neq 4\\\end{cases}$
b) $M = \bigg(\dfrac{\sqrt x}{\sqrt x - 2} + \dfrac{\sqrt x}{\sqrt x + 2}\bigg) . \dfrac{x - 4}{\sqrt{4x}} (ĐKXĐ: x > 0 ; x \neq 4)$
$= \dfrac{\sqrt x(\sqrt x + 2) + \sqrt x(\sqrt x - 2)}{(\sqrt x + 2)(\sqrt x -2)} . \dfrac{x - 4}{\sqrt{4x}}$
$=\dfrac{x + 2\sqrt x + x - 2\sqrt x}{x - 4} . \dfrac{x-4}{\sqrt{4x}}$
$=2x . \dfrac{1}{2\sqrt x}$
$=\sqrt x$
