$a/P=$$(\dfrac{1}{\sqrt{x}-1}-\dfrac{1}{\sqrt{x}}):$$(\dfrac{\sqrt{x}+1}{\sqrt{x}-2}-\dfrac{\sqrt{x}+2}{\sqrt{x}-1})$
$P=$$\dfrac{\sqrt{x}-(\sqrt{x}-1)}{\sqrt{x}(\sqrt{x}-1)}:$$\dfrac{(\sqrt{x}+1)(\sqrt{x}-1)-(\sqrt{x}+2)(\sqrt{x}-2)}{(\sqrt{x}-1)(\sqrt{x}-2)}$
$P=$$\dfrac{1}{\sqrt{x}(\sqrt{x}+1)}.$ $\dfrac{(\sqrt{x}-2)(\sqrt{x}-1)}{3}$
$P=\dfrac{1}{\sqrt{x}}.$ $\dfrac{\sqrt{x}-2}{3}$
$P=\dfrac{\sqrt{x}-2}{3\sqrt{x}}$
$b/$ Để $P$ có giá trị âm thì $P<0$
$⇔$$\dfrac{\sqrt{x}-2}{3\sqrt{x}}<0$
$⇔\sqrt{x}-2<0$
$⇔\sqrt{x}<2$
$⇔{x}<4$
Theo đề có đkxđ là $x>0 ; $$x\neq1;x$$\neq4$
Vậy $0<x<4$ ;$x\neq1$ thì P có giá trị âm
