Đáp án:
$\begin{array}{l}
E = \dfrac{{\sqrt a + \sqrt b - 1}}{{a + \sqrt {ab} }} + \dfrac{{\sqrt a - \sqrt b }}{{2\sqrt {ab} }}.\left( {\dfrac{{\sqrt b }}{{a - \sqrt {ab} }} + \dfrac{{\sqrt b }}{{a + \sqrt {ab} }}} \right)\\
= \dfrac{{\sqrt a + \sqrt b - 1}}{{\sqrt a \left( {\sqrt a + \sqrt b } \right)}}\\
+ \dfrac{{\sqrt a - \sqrt b }}{{2\sqrt {ab} }}.\sqrt b .\dfrac{{\sqrt a + \sqrt b + \sqrt a - \sqrt b }}{{\sqrt a \left( {\sqrt a - \sqrt b } \right)\left( {\sqrt a + \sqrt b } \right)}}\\
= \dfrac{{\sqrt a + \sqrt b - 1}}{{\sqrt a \left( {\sqrt a + \sqrt b } \right)}} + \dfrac{1}{{2\sqrt a }}.\dfrac{{2\sqrt a }}{{\sqrt a \left( {\sqrt a + \sqrt b } \right)}}\\
= \dfrac{{\sqrt a + \sqrt b - 1}}{{\sqrt a \left( {\sqrt a + \sqrt b } \right)}} + \dfrac{1}{{\sqrt a \left( {\sqrt a + \sqrt b } \right)}}\\
= \dfrac{{\sqrt a + \sqrt b }}{{\sqrt a \left( {\sqrt a + \sqrt b } \right)}}\\
= \dfrac{1}{{\sqrt a }}
\end{array}$
