Giải thích các bước giải:

a.Ta có:
$A=(\dfrac{x+2\sqrt{x}}{\sqrt{x}+2}-\dfrac{\sqrt{x}-1}{x-\sqrt{x}}):\dfrac{\sqrt{x}+1}{x}$

$\to A=(\dfrac{\sqrt{x}(\sqrt{x}+2)}{\sqrt{x}+2}-\dfrac{\sqrt{x}-1}{\sqrt{x}(\sqrt{x}-1)}\cdot \dfrac{x}{\sqrt{x}+1}$

$\to A=(\sqrt{x}-\dfrac1{\sqrt{x}})\cdot \dfrac{x}{\sqrt{x}+1}$

$\to A=\dfrac{x-1}{\sqrt{x}}\cdot \dfrac{x}{\sqrt{x}+1}$

$\to A=\dfrac{(\sqrt{x}+1)(\sqrt{x}-1)}{\sqrt{x}}\cdot \dfrac{x}{\sqrt{x}+1}$

$\to A=\sqrt{x}(\sqrt{x}-1)$

$\to A=x-\sqrt{x}$

b.Ta có:

$P=x-\sqrt{x}-4\sqrt{x}$

$\to P=x-5\sqrt{x}$

$\to P=(\sqrt{x}-\dfrac52)^2-\dfrac{25}4\ge\dfrac{-25}4$

$\to GTNN_P=-\dfrac{25}4$

Dấu = xảy ra khi $\sqrt{x}=\dfrac52\to x=\dfrac{25}4$