Question

$x = \frac{1}{2 - \sqrt{3} } then \: the \: value \: of ( x - \frac{1}{x} is$
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Answer 1

Answer:

$x - \frac{1}{x} = \frac{6 - 4 \sqrt{3} }{2 - \sqrt{3} }$

Step by step explanation:

$x = \frac{1}{2 - \sqrt{3} } \\ x - \frac{1}{x} \\ = \frac{1}{2 - \sqrt{3} } - \frac{1}{ \frac{1}{2 - \sqrt{3} } } \\ = \frac{1}{2 - \sqrt{3} } - 2 - \sqrt{3} \\ = \frac{1 - {(2 - \sqrt{3} )}^{2} }{2 - \sqrt{3} } \\ = \frac{1 - (4 + 3 - 4 \sqrt{3} )}{2 - \sqrt{3} } \\ = \frac{1 - 4 - 3 + 4 \sqrt{3} }{2 - \sqrt{3} } \\ = \frac{( - 6) + 4 \sqrt{3} }{2 - \sqrt{3} } \\ = \frac{6 - 4 \sqrt{3} }{2 - \sqrt{3} }$