\[\begin{array}{l}
a)\,\,\,A = \frac{{x - 2\sqrt x + 1}}{{\sqrt x - 1}} + \frac{{x\sqrt x + 1}}{{x - \sqrt x + 1}} + 1\,\,\,\left( {x \ge 0,\,\,x \ne 1} \right)\\
= \frac{{{{\left( {\sqrt x - 1} \right)}^2}}}{{\sqrt x - 1}} + \frac{{\left( {\sqrt x + 1} \right)\left( {x - \sqrt x + 1} \right)}}{{x - \sqrt x + 1}}\\
= \sqrt x - 1 + \sqrt x + 1 + 1\\
= 2\sqrt x + 1.\\
b)\,\,\,B = \left[ {\frac{{x + 3}}{{x - 9}} - \frac{1}{{\sqrt 3 }}} \right]:\frac{{\sqrt x }}{{\sqrt x - 3}}\,\,\,\,\,\left( {x > 0,\,\,\,x \ne 9} \right)\\
= \frac{{\sqrt 3 x + 3\sqrt 3 - x + 9}}{{\sqrt 3 \left( {\sqrt x - 3} \right)\left( {\sqrt x + 3} \right)}}.\frac{{\sqrt x - 3}}{{\sqrt x }}\\
= \frac{{\left( {\sqrt 3 - 1} \right)x + 3\sqrt 3 + 9}}{{\sqrt 3 \left( {\sqrt x + 3} \right)\sqrt x }}.
\end{array}\]
