Giải thích các bước giải:
Ta có:
\(\begin{array}{l}
\left( {\sqrt a + \dfrac{{b - \sqrt {ab} }}{{\sqrt a + \sqrt b }}} \right):\left( {\dfrac{a}{{\sqrt {ab} }} + \dfrac{b}{{\sqrt {ab} - a}} - \dfrac{{a + b}}{{\sqrt {ab} }}} \right)\,\,\,\,\,\,\,\,\,\,\left( {a,b > 0} \right)\\
= \dfrac{{\sqrt a .\left( {\sqrt a + \sqrt b } \right) + b - \sqrt {ab} }}{{\sqrt a + \sqrt b }}:\left[ {\left( {\dfrac{a}{{\sqrt {ab} }} - \dfrac{{a + b}}{{\sqrt {ab} }}} \right) + \dfrac{b}{{\sqrt {ab} - a}}} \right]\\
= \dfrac{{a + \sqrt {ab} + b - \sqrt {ab} }}{{\sqrt a + \sqrt b }}:\left[ {\dfrac{{ - b}}{{\sqrt {ab} }} + \dfrac{b}{{\sqrt a \left( {\sqrt b - \sqrt a } \right)}}} \right]\\
= \dfrac{{a + b}}{{\sqrt a + \sqrt b }}:\dfrac{{ - b.\left( {\sqrt b - \sqrt a } \right) + b.\sqrt b }}{{\sqrt a .\sqrt b .\left( {\sqrt b - \sqrt a } \right)}}\\
= \dfrac{{a + b}}{{\sqrt a + \sqrt b }}:\dfrac{{ - b\sqrt b + b\sqrt a + b\sqrt b }}{{\sqrt {ab} \left( {\sqrt b - \sqrt a } \right)}}\\
= \dfrac{{a + b}}{{\sqrt a + \sqrt b }}:\dfrac{{b\sqrt a }}{{\sqrt {ab} \left( {\sqrt b - \sqrt a } \right)}}\\
= \dfrac{{a + b}}{{\sqrt a + \sqrt b }}:\dfrac{{\sqrt b }}{{\sqrt b - \sqrt a }}\\
= \dfrac{{a + b}}{{\sqrt a + \sqrt b }}.\dfrac{{\sqrt b - \sqrt a }}{{\sqrt b }}\\
= \dfrac{{\left( {a + b} \right)\left( {\sqrt b - \sqrt a } \right)}}{{\sqrt b \left( {\sqrt a + \sqrt b } \right)}}
\end{array}\)
