Đáp án:
$P=\dfrac{1}{\sqrt{x}(\sqrt{x}+1)}$
Giải thích các bước giải:
$P=\left(\dfrac{x-1}{\sqrt{x}+1}-\dfrac{x-2\sqrt{x}+1}{x-\sqrt{x}}+1\right).\dfrac{1}{x\sqrt{x}+1}\\ =\left(\dfrac{(x-1)(x-\sqrt{x})}{(\sqrt{x}+1)(x-\sqrt{x})}-\dfrac{(\sqrt{x}+1)(x-2\sqrt{x}+1)}{(\sqrt{x}+1)(x-\sqrt{x})}+\dfrac{(\sqrt{x}+1)(x-\sqrt{x})}{(\sqrt{x}+1)(x-\sqrt{x})}\right).\dfrac{1}{x\sqrt{x}+1}\\ =\dfrac{x^2-x\sqrt{x}+\sqrt{x}-1}{\sqrt{x}(\sqrt{x}+1)(\sqrt{x}-1)}.\dfrac{1}{x\sqrt{x}+1}\\ =\dfrac{x\sqrt{x}(\sqrt{x}-1)+\sqrt{x}-1}{\sqrt{x}(\sqrt{x}+1)(\sqrt{x}-1)(x\sqrt{x}+1)}\\ =\dfrac{(x\sqrt{x}+1)(\sqrt{x}-1)}{\sqrt{x}(\sqrt{x}+1)(\sqrt{x}-1)(x\sqrt{x}+1)}\\ =\dfrac{1}{\sqrt{x}(\sqrt{x}+1)}$