Giải thích các bước giải:
Ta có:
$P=\left(\dfrac{2\sqrt{x}-x}{x\sqrt{x}-1}+\dfrac{1}{\sqrt{x}-1}\right):\left(1+\dfrac{\sqrt{x}+2}{x+\sqrt{x}+1}\right)$
$\to P=\left(\dfrac{2\sqrt{x}-x}{\left(\sqrt{x}-1\right)\left(x+\sqrt{x}+1\right)}+\dfrac{x+\sqrt{x}+1}{\left(\sqrt{x}-1\right)\left(x+\sqrt{x}+1\right)}\right):\dfrac{x+\sqrt{x}+1+\sqrt{x}+2}{x+\sqrt{x}+1}$
$\to P=\dfrac{2\sqrt{x}-x+x+\sqrt{x}+1}{\left(\sqrt{x}-1\right)\left(x+\sqrt{x}+1\right)}:\dfrac{x+2\sqrt{x}+3}{x+\sqrt{x}+1}$
$\to P=\dfrac{3\sqrt{x}+1}{\left(\sqrt{x}-1\right)\left(x+\sqrt{x}+1\right)}\cdot \dfrac{x+\sqrt{x}+1}{x+2\sqrt{x}+3}$
$\to P=\dfrac{3\sqrt{x}+1}{\left(\sqrt{x}-1\right)\left(x+2\sqrt{x}+3\right)}$
