Simplify ( \(\frac{1}{2 - √3}\) + \(\frac{2}{2 + √3}\) )\(^{-1}\)
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Correct Answer: Option 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)\(^{-1}\)
= \(\frac{1}{6 - √3}\)
= \(\frac{6 + √3}{6 - √3 * 6 + √3}\)
= \(\frac{6 + √3}{33}\)
( \(\frac{1}{2 - √3}\) + \(\frac{2}{2 + √3}\) )\(^{-1}\)
= \(\frac{2 + √3 + 2(2 - √3)}{(2 - √3)(2 + √3)}\)
= 2 + √3 + 4 - 2√3
= (6 - √3)\(^{-1}\)
= \(\frac{1}{6 - √3}\)
= \(\frac{6 + √3}{6 - √3 * 6 + √3}\)
= \(\frac{6 + √3}{33}\)