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