Simplify ( \(\frac{1}{2 – √3}\) + \(\frac{2}{2 + √3}\) )\(^{-1}\)
- \(\frac{-1}{33}\)(6 + √3)
- \(\frac{-1}{33}\)(6 - √3)
-
\(\frac{1}{33}\)(6 + √3)
- \(\frac{1}{33}\)(6 - √3)
The correct answer is: C
Explanation
( \(\frac{1}{2 - √3}\) + \(\frac{2}{2 + √3}\) )\(^{-1}\)
= \(\frac{2 + √3 + 2(2 - √3)}{(2 - √3)(2 + √3)}\)
= 2 + √3 + 4 - 2√3
= (6 - √3)\(^{-1}\)
= \(\frac{1}{6 - √3}\)
= \(\frac{6 + √3}{6 - √3 * 6 + √3}\)
= \(\frac{6 + √3}{33}\)