Đáp án:
\(\dfrac{{a - 2\sqrt {ab} + b}}{{ - \left( {a - \sqrt {ab} + b} \right)}}\)
Giải thích các bước giải:
\(\begin{array}{l}
DK:a > 0;b > 0\\
\left( {\dfrac{{\sqrt a + \sqrt b }}{{\sqrt a - \sqrt b }} - \dfrac{{4\sqrt {ab} }}{{a - b}}} \right).\dfrac{{a\sqrt a + b\sqrt b }}{{\sqrt {ab} - a - b}}\\
= \left[ {\dfrac{{{{\left( {\sqrt a + \sqrt b } \right)}^2} - 4\sqrt {ab} }}{{\left( {\sqrt a - \sqrt b } \right)\left( {\sqrt a + \sqrt b } \right)}}} \right].\dfrac{{\left( {\sqrt a + \sqrt b } \right)\left( {\sqrt a - \sqrt b } \right)}}{{ - \left( {a - \sqrt {ab} + b} \right)}}\\
= \dfrac{{a + 2\sqrt {ab} + b - 4\sqrt {ab} }}{{\left( {\sqrt a - \sqrt b } \right)\left( {\sqrt a + \sqrt b } \right)}}.\dfrac{{\left( {\sqrt a + \sqrt b } \right)\left( {\sqrt a - \sqrt b } \right)}}{{ - \left( {a - \sqrt {ab} + b} \right)}}\\
= \dfrac{{a - 2\sqrt {ab} + b}}{{ - \left( {a - \sqrt {ab} + b} \right)}}
\end{array}\)
