Đáp án:
$\begin{array}{l}\left(\dfrac{1}{\sqrt{x}-1}-\dfrac{1}{\sqrt{x}}\right):\left(\dfrac{\sqrt{x}+1}{\sqrt{x}-2}-\dfrac{\sqrt{x}+2}{\sqrt{x}-1}\right)\\=\dfrac{\sqrt{x}-\sqrt{x}+1}{\sqrt{x}(\sqrt{x}-1)}:\dfrac{(\sqrt{x}-1)(\sqrt{x}+1)-(\sqrt{x}-2)(\sqrt{x}+2)}{(\sqrt{x}-2)(\sqrt{x}-1)}\\=\dfrac{1}{\sqrt{x}(\sqrt{x}-1)}:\dfrac{x-1-x+4}{(\sqrt{x}-2)(\sqrt{x}-1)}\\=\dfrac{1}{\sqrt{x}(\sqrt{x}-1)}:\dfrac{3}{(\sqrt{x}-2)(\sqrt{x}-1)}\\=\dfrac{1}{\sqrt{x}(\sqrt{x}-1)}\times\dfrac{(\sqrt{x}-2)(\sqrt{x}-1)}{3}\\=\dfrac{1}{\sqrt{x}}\times\dfrac{\sqrt{x}-2}{3}\\=\dfrac{\sqrt{x}-2}{3\sqrt{x}}\end{array}$