Giải thích các bước giải:
Ta có:
\(\begin{array}{l}
1,\\
DKXD:\,\,\,\left\{ \begin{array}{l}
a \ge 0\\
a \ne 1
\end{array} \right.\\
\left( {\dfrac{{1 - a\sqrt a }}{{1 - \sqrt a }} + \sqrt a } \right).{\left( {\dfrac{{1 - \sqrt a }}{{1 - a}}} \right)^2}\\
= \left( {\dfrac{{\left( {1 - \sqrt a } \right)\left( {1 + \sqrt a + a} \right)}}{{1 - \sqrt a }} + \sqrt a } \right).{\left( {\dfrac{{1 - \sqrt a }}{{\left( {1 - \sqrt a } \right)\left( {1 + \sqrt a } \right)}}} \right)^2}\\
= \left( {\left( {1 + \sqrt a + a} \right) + \sqrt a } \right).{\left( {\dfrac{1}{{\left( {1 + \sqrt a } \right)}}} \right)^2}\\
= \left( {a + 2\sqrt a + 1} \right).\dfrac{1}{{{{\left( {1 + \sqrt a } \right)}^2}}}\\
= {\left( {\sqrt a + 1} \right)^2}.\dfrac{1}{{{{\left( {1 + \sqrt a } \right)}^2}}}\\
= 1\\
2,\\
DKXD:\,\,\,\,\left\{ \begin{array}{l}
a > 0\\
a \ne 1
\end{array} \right.\\
\left( {\dfrac{1}{{a - \sqrt a }} + \dfrac{1}{{\sqrt a - 1}}} \right):\dfrac{{\sqrt a + 1}}{{a - 2\sqrt a + 1}}\\
= \left( {\dfrac{1}{{\sqrt a \left( {\sqrt a - 1} \right)}} + \dfrac{1}{{\sqrt a - 1}}} \right):\dfrac{{\sqrt a + 1}}{{{{\left( {\sqrt a - 1} \right)}^2}}}\\
= \dfrac{{1 + \sqrt a }}{{\sqrt a \left( {\sqrt a - 1} \right)}}:\dfrac{{\sqrt a + 1}}{{{{\left( {\sqrt a - 1} \right)}^2}}}\\
= \dfrac{{1 + \sqrt a }}{{\sqrt a \left( {\sqrt a - 1} \right)}}.\dfrac{{{{\left( {\sqrt a - 1} \right)}^2}}}{{\sqrt a + 1}}\\
= \dfrac{{\sqrt a - 1}}{{\sqrt a }}
\end{array}\)
