Đáp án:
\[4\sqrt {ab} \]
Giải thích các bước giải:
ĐKXĐ: \(a \ne b\)
Ta có:
\(\begin{array}{l}
A = \left( {\frac{{\sqrt a + \sqrt b }}{{\sqrt a - \sqrt b }} - \frac{{\sqrt a - \sqrt b }}{{\sqrt a + \sqrt b }}} \right)\left( {a - b} \right)\\
= \frac{{\left( {\sqrt a + \sqrt b } \right)\left( {\sqrt a + \sqrt b } \right) - \left( {\sqrt a - \sqrt b } \right)\left( {\sqrt a - \sqrt b } \right)}}{{\left( {\sqrt a - \sqrt b } \right)\left( {\sqrt a + \sqrt b } \right)}}\left( {a - b} \right)\\
= \frac{{{{\left( {\sqrt a + \sqrt b } \right)}^2} - {{\left( {\sqrt a - \sqrt b } \right)}^2}}}{{{{\left( {\sqrt a } \right)}^2} - {{\left( {\sqrt b } \right)}^2}}}\left( {a - b} \right)\\
= \frac{{a + 2\sqrt {ab} + b - a + 2\sqrt {ab} - b}}{{a - b}}\left( {a - b} \right)\\
= 4\sqrt {ab}
\end{array}\)
