a. $P = (\dfrac{1}{\sqrt{x} + 1} - \dfrac{1}{x + \sqrt{x}}) : \dfrac{x - \sqrt{x} + 1}{x\sqrt{x} + 1}$
$P = [\dfrac{\sqrt{x} - 1}{\sqrt{x}(\sqrt{x} + 1)}] : \dfrac{x - \sqrt{x} + 1}{(\sqrt{x} + 1)(x - \sqrt{x} + 1)}$
$P = \dfrac{\sqrt{x} - 1}{\sqrt{x}(\sqrt{x} + 1)} : \dfrac{1}{\sqrt{x} + 1}$
$P = \dfrac{\sqrt{x} - 1}{\sqrt{x}(\sqrt{x} + 1}.(\sqrt{x} + 1) = \dfrac{\sqrt{x} - 1}{\sqrt{x}}$
b. Vì $\sqrt{x} > 0$ với mọi x > 0 nên:
$P < 0 \to \sqrt{x} - 1 < 0 \to \sqrt{x} < 1 \to 0 < x < 1$
Vậy với $0 < x < 1$ thì $P < 0$
