Rút gọn các biểu thức sau:a) (sqrt {48a} .

a) \(\sqrt {48a} .\sqrt {3a}  - 2a\) với \(a \ge 0\)

\( = \sqrt {48a.3a}  - 2a = \sqrt {3.16a.3a}  - 2a\)

\(\begin{array}{l}
 = \sqrt {{3^2}} .\sqrt {16} .\sqrt {{a^2}}  - 2a\\
 = 3.4a - 2a = 0
\end{array}\)

b) \(\frac{{\sqrt x  + \sqrt y }}{{\sqrt x  - \sqrt y }} + \frac{{\sqrt x  - \sqrt y }}{{\sqrt x  + \sqrt y }} - \frac{{4y}}{{x - y}}\)

\(\begin{array}{l}
 = \frac{{{{\left( {\sqrt x  + \sqrt y } \right)}^2}}}{{x - y}} + \frac{{{{\left( {\sqrt x  - \sqrt y } \right)}^2}}}{{x - y}} - \frac{{4y}}{{x - y}}\\
 = \frac{{x + y + 2\sqrt {xy}  + x + y - 2\sqrt {xy}  - 4y}}{{x - y}}\\
 = \frac{{2x - 2y}}{{x - y}} = \frac{{2\left( {x - y} \right)}}{{x - y}} = 2
\end{array}\)