Question

How do you simplify 2−√ ​3 /​ ​2+√ ​3 ​ − ​2+√ ​3/ ​2−√ ​3 ​ ​​ ​​

Answer 1

$= > \frac{2 - \sqrt{3} }{2 + \sqrt{3} } - \frac{2 + \sqrt{3} }{2 - \sqrt{3} } \\ \\ \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \underline{ By \: \: Rationalization, } \\ \\ \\ \\ = > \huge{(} \small{\frac{2 - \sqrt{3} }{2 + \sqrt{3} } } \times \frac{2 - \sqrt{3} }{2 - \sqrt{3} } \huge{)} \: \large{ - } \: \huge{(} \small{ \frac{2 + \sqrt{3} }{2 - \sqrt{3} } \times \frac{2 + \sqrt{3} }{2 + \sqrt{3} } } \huge{)} \\ \\ \\ \\ = > \huge{(} \small{ \frac{(2 - \sqrt{3} ) ^{2} }{ {(2)}^{2} - {( \sqrt{3} )}^{2} } } \huge{)} \small{ - } \huge{(}\small{ \frac{ {(2 + \sqrt{3} )}^{2} }{ {(2)}^{2} - {( \sqrt{3}) }^{2} } } \huge{)} \\ \\ \\ \\ = > \frac{4 + 3 - 4 \sqrt{3} }{4 - 3} - \frac{4 + 3 + 4 \sqrt{3} }{4 - 3} \\ \\ \\ \\ = > \frac{7 - 4 \sqrt{3} }{ 1} - \frac{7 + 4 \sqrt{3} }{1} \\ \\ \\ = > 7 - 4 \sqrt{3} - 7 - 4 \sqrt{3} \\ \\ \\ = - 4 \sqrt{3} - 4\sqrt{3}\\ \\ \\ = > - 8\sqrt{3}$

Answer 2

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