Giải thích các bước giải:
$A = \left ( \dfrac{\sqrt{a}}{\sqrt{a} + \sqrt{b}} + \dfrac{a}{b - a} \right ) : \left ( \dfrac{\sqrt{a}}{\sqrt{a} + \sqrt{b}} + \dfrac{a}{a + b + 2\sqrt{ab}} \right )$ (ĐK $a \geq 0, b \geq 0, a \neq b$)
$= \left ( \dfrac{\sqrt{a}}{\sqrt{a} + \sqrt{b}} - \dfrac{a}{a - b} \right ) : \left [ \dfrac{\sqrt{a}}{\sqrt{a} + \sqrt{b}} + \dfrac{a}{\left ( \sqrt{a} + \sqrt{b} \right )^{2}} \right ]$
$= \left [ \dfrac{\sqrt{a}}{\sqrt{a} + \sqrt{b}} - \dfrac{a}{\left ( \sqrt{a} + \sqrt{b} \right )\left ( \sqrt{a} - \sqrt{b} \right )} \right ] : \dfrac{\sqrt{a}.\left ( \sqrt{a} + \sqrt{b} \right ) + a}{\left ( \sqrt{a} + \sqrt{b} \right )^{2}}$
$= \dfrac{\sqrt{a}.\left ( \sqrt{a} - \sqrt{b} \right ) - a}{\left ( \sqrt{a} + \sqrt{b} \right )\left ( \sqrt{a} - \sqrt{b} \right )}.\dfrac{\left ( \sqrt{a} + \sqrt{b} \right )^{2}}{\sqrt{a}.\left ( \sqrt{a} + \sqrt{b} \right ) + a}$
$= \dfrac{\sqrt{a}.\left ( \sqrt{a} - \sqrt{b} - \sqrt{a}\right )}{\left ( \sqrt{a} + \sqrt{b} \right )\left ( \sqrt{a} - \sqrt{b} \right )}.\dfrac{\left ( \sqrt{a} + \sqrt{b} \right )^{2}}{\sqrt{a}.\left ( \sqrt{a} + \sqrt{b} + \sqrt{a}\right )}$
$= \dfrac{\sqrt{b}\left ( \sqrt{a} + \sqrt{b} \right )}{\left ( \sqrt{b} - \sqrt{a} \right )\left ( 2\sqrt{a} + \sqrt{b} \right )}$
