Đáp án:
$\begin{array}{l}
2.1\\
\sqrt 3 - \sqrt {48} + \sqrt {75} \\
= \sqrt 3 - 4\sqrt 3 + 5\sqrt 3 \\
= 2\sqrt 3 \\
2.2\\
a)P = \left( {\dfrac{{\sqrt x }}{{\sqrt x + 3}} + \dfrac{3}{{\sqrt x - 3}}} \right):\dfrac{{x + 9}}{{\sqrt x + 3}}\\
= \dfrac{{\sqrt x \left( {\sqrt x - 3} \right) + 3\left( {\sqrt x + 3} \right)}}{{\left( {\sqrt x + 3} \right)\left( {\sqrt x - 3} \right)}}.\dfrac{{\sqrt x + 3}}{{x + 9}}\\
= \dfrac{{x - 3\sqrt x + 3\sqrt x + 9}}{{\sqrt x - 3}}.\dfrac{1}{{x + 9}}\\
= \dfrac{1}{{\sqrt x - 3}}\\
b)x = 16\left( {tmdk} \right)\\
\Leftrightarrow \sqrt x = 4\\
\Leftrightarrow P = \dfrac{1}{{4 - 3}} = 1\\
34)\\
Dkxd:x > 0;x\# 1\\
a)P = \left( {\dfrac{{\sqrt x }}{{\sqrt x - 1}} - \dfrac{1}{{\sqrt x + 1}}} \right):\left( {\dfrac{1}{{\sqrt x + 1}} + \dfrac{2}{{x - 1}}} \right)\\
= \dfrac{{\sqrt x \left( {\sqrt x + 1} \right) - \sqrt x + 1}}{{\left( {\sqrt x - 1} \right)\left( {\sqrt x + 1} \right)}}:\dfrac{{\sqrt x - 1 + 2}}{{\left( {\sqrt x - 1} \right)\left( {\sqrt x + 1} \right)}}\\
= \dfrac{{x + \sqrt x - \sqrt x + 1}}{{\left( {\sqrt x - 1} \right)\left( {\sqrt x + 1} \right)}}.\dfrac{{\left( {\sqrt x - 1} \right)\left( {\sqrt x + 1} \right)}}{{\sqrt x + 1}}\\
= \dfrac{{x + 1}}{{\sqrt x + 1}}\\
b)x = 4 - 2\sqrt 3 \left( {tmdk} \right)\\
= {\left( {\sqrt 3 - 1} \right)^2}\\
\Leftrightarrow \sqrt x = \sqrt 3 - 1\\
P = \dfrac{{x + 1}}{{\sqrt x + 1}} = \dfrac{{4 - 2\sqrt 3 + 1}}{{\sqrt 3 - 1 + 1}}\\
= \dfrac{{5 - 2\sqrt 3 }}{{\sqrt 3 }}\\
= \dfrac{{5\sqrt 3 - 6}}{3}
\end{array}$
