$a,$ $P=\left(\dfrac{1}{\sqrt{x}-2}+\dfrac{1}{\sqrt{x}+2}\right):\dfrac{2x}{x-4}$
$=\dfrac{\left(\dfrac{1}{\sqrt{x}-2}+\dfrac{1}{\sqrt{x}+2}\right)\left(x-4\right)}{2x}$
$=\dfrac{2\sqrt{x}}{2x}$
$=\dfrac{\sqrt{x}}{\sqrt{x}\sqrt{x}}$
$=\dfrac{1}{\sqrt{x}}$
$b,$ Thay `x=7+4\sqrt{3}` vào `P` ta được:
$\:\dfrac{1}{\sqrt{7+4\sqrt{3}}}$
$=\dfrac{1}{1.\sqrt{3}+2}$
$=\dfrac{1}{\sqrt{3}+2}$
$=\dfrac{1. \left(\sqrt{3}-2\right)}{\left(\sqrt{3}+2\right)\left(\sqrt{3}-2\right)}$
$=\dfrac{\sqrt{3}-2}{-1}$
$=\dfrac{\sqrt{3}-2}{-1}$
$=2-\sqrt{3}$
`⇒` Với `x=7+4\sqrt{3}` thì `P` $=2-\sqrt{3}$
