\(\begin{array}{l}
\left( {\frac{1}{{a - \sqrt a }} + \frac{1}{{\sqrt a - 1}}} \right):\frac{{\sqrt a + 1}}{{a - 2\sqrt a + 1}}\\
= \left[{\frac{1}{{\sqrt a (\sqrt a - 1)}} + \frac{1}{{\sqrt a - 1}}} \right]:\frac{{\sqrt a + 1}}{{{{\left( {\sqrt a - 1} \right)}^2}}}\\
= \frac{{1 + \sqrt a }}{{\sqrt a (\sqrt a - 1)}}.\frac{{{{\left( {\sqrt a - 1} \right)}^2}}}{{\sqrt a + 1}}\\
= \frac{{\sqrt a - 1}}{{\sqrt a }}
\end{array}\)
