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1. Simplify : $(\frac{\frac{3}{2 + \sqrt{3}} - \frac{2}{2 - \sqrt{3}}}{2 - 5 \sqrt{3}}) = ?$

A. $\frac{1}{2} - 5 \sqrt{3}$

B. 2 - $5 \sqrt{3}$

C. 1

D. 0

Solution:

\begin{aligned} \frac{\frac{3}{2 + \sqrt{3}} - \frac{2}{2 - \sqrt{3}}}{2 - 5 \sqrt{3}} \\ = \frac{\frac{3 (2 - \sqrt{3}) - 2 (2 + \sqrt{3})}{(2 + \sqrt{3}) (2 - \sqrt{3})}}{2 - 5 \sqrt{3}} \\ = \frac{6 - 3 \sqrt{3} - 4 - 2 \sqrt{3}}{(2 + \sqrt{3}) (2 - \sqrt{3}) (2 - 5 \sqrt{3})} \\ = \frac{2 - 5 \sqrt{3}}{2 - 5 \sqrt{3}} \\ = 1 \end{aligned}

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