Giải thích các bước giải:

 Ta có:

\(\begin{array}{l}
a,\\
A = \left( {\dfrac{{\sqrt x }}{{3 + \sqrt x }} + \dfrac{{x + 9}}{{9 - x}}} \right):\left( {\dfrac{{3\sqrt x  + 1}}{{x - 3\sqrt x }} - \dfrac{1}{{\sqrt x }}} \right)\,\,\,\,\,\,\,\,\left( {x > 0,\,\,x \ne 9} \right)\\
 = \left( {\dfrac{{\sqrt x }}{{3 + \sqrt x }} + \dfrac{{x + 9}}{{\left( {3 - \sqrt x } \right)\left( {3 + \sqrt x } \right)}}} \right):\left( {\dfrac{{3\sqrt x  + 1}}{{\sqrt x \left( {\sqrt x  - 3} \right)}} - \dfrac{1}{{\sqrt x }}} \right)\\
 = \dfrac{{\sqrt x \left( {3 - \sqrt x } \right) + x + 9}}{{\left( {3 - \sqrt x } \right)\left( {3 + \sqrt x } \right)}}:\dfrac{{3\sqrt x  + 1 - \left( {\sqrt x  - 3} \right)}}{{\sqrt x \left( {\sqrt x  - 3} \right)}}\\
 = \dfrac{{3\sqrt x  - x + x + 9}}{{\left( {3 - \sqrt x } \right)\left( {3 + \sqrt x } \right)}}:\dfrac{{3\sqrt x  + 1 - \sqrt x  + 3}}{{\sqrt x \left( {\sqrt x  - 3} \right)}}\\
 = \dfrac{{3.\left( {\sqrt x  + 3} \right)}}{{\left( {3 - \sqrt x } \right)\left( {3 + \sqrt x } \right)}}:\dfrac{{2\left( {\sqrt x  + 2} \right)}}{{\sqrt x \left( {\sqrt x  - 3} \right)}}\\
 = \dfrac{3}{{\left( {3 - \sqrt x } \right)}}.\dfrac{{\sqrt x \left( {\sqrt x  - 3} \right)}}{{2\left( {\sqrt x  + 2} \right)}}\\
 = \dfrac{{ - 3\sqrt x }}{{2\left( {\sqrt x  + 2} \right)}}\\
B = \dfrac{{\sqrt x }}{{\sqrt x  - 1}} - \dfrac{{2\sqrt x  - 1}}{{\sqrt x \left( {\sqrt x  - 1} \right)}}\,\,\,\,\,\,\,\,\,\,\,\,\left( {x > 0,\,\,x \ne 1} \right)\\
 = \dfrac{{{{\sqrt x }^2} - \left( {2\sqrt x  - 1} \right)}}{{\sqrt x \left( {\sqrt x  - 1} \right)}}\\
 = \dfrac{{x - 2\sqrt x  + 1}}{{\sqrt x \left( {\sqrt x  - 1} \right)}}\\
 = \dfrac{{{{\left( {\sqrt x  - 1} \right)}^2}}}{{\sqrt x \left( {\sqrt x  - 1} \right)}}\\
 = \dfrac{{\sqrt x  - 1}}{{\sqrt x }}\\
C = \dfrac{{\sqrt x }}{{\sqrt x  + \sqrt y }} - \dfrac{{\sqrt y }}{{\sqrt y  - \sqrt x }} - \dfrac{{2\sqrt {xy} }}{{x - y}}\,\,\,\,\,\left( {x \ne y \ge 0} \right)\\
 = \dfrac{{\sqrt x }}{{\sqrt x  + \sqrt y }} + \dfrac{{\sqrt y }}{{\sqrt x  - \sqrt y }} - \dfrac{{2\sqrt {xy} }}{{\left( {\sqrt x  - \sqrt y } \right)\left( {\sqrt x  + \sqrt y } \right)}}\\
 = \dfrac{{\sqrt x \left( {\sqrt x  - \sqrt y } \right) + \sqrt y \left( {\sqrt x  + \sqrt y } \right) - 2\sqrt {xy} }}{{\left( {\sqrt x  - \sqrt y } \right)\left( {\sqrt x  + \sqrt y } \right)}}\\
 = \dfrac{{x - \sqrt {xy}  + \sqrt {xy}  + y - 2\sqrt {xy} }}{{\left( {\sqrt x  - \sqrt y } \right)\left( {\sqrt x  + \sqrt y } \right)}}\\
 = \dfrac{{x - 2\sqrt {xy}  + y}}{{\left( {\sqrt x  - \sqrt y } \right)\left( {\sqrt x  + \sqrt y } \right)}}\\
 = \dfrac{{{{\left( {\sqrt x  - \sqrt y } \right)}^2}}}{{\left( {\sqrt x  - \sqrt y } \right)\left( {\sqrt x  + \sqrt y } \right)}}\\
 = \dfrac{{\sqrt x  - \sqrt y }}{{\sqrt x  + \sqrt y }}
\end{array}\)