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