Question

simplify
$\frac{2 + \sqrt{3} }{2 - \sqrt{3} } + \frac{2 \sqrt{3} }{2 + \sqrt{3} }\ \textless \ br /\ \textgreater$

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Answer 1

$\huge\underline\mathbb\orange{ANSWER}$

The answer is attached~ Please excuse the bad handwriting, it was written in a hurry. ^^"

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Answer 2

$\huge \bf \underline{ \underline{Question}}$

$\frac{2 + \sqrt{3} }{2 - \sqrt{3} } + \frac{2 \sqrt{3} }{2 + \sqrt{3} }$

$\huge \bf \underline{ \underline{Solution}}$

$=\frac{2 + \sqrt{3} }{2 - \sqrt{3} } + \frac{2 \sqrt{3} }{2 + \sqrt{3} } \\ = \frac{(2 + \sqrt{3} )^{2} + 2 \sqrt{3}(2 - \sqrt{3} )}{(2 - \sqrt{3})(2 + \sqrt{3}) } \\ = \frac{4 + 3 + 4 \sqrt{3} + 4 \sqrt{3} - 6}{4 - 3} \\ = 1 + 8 \sqrt{3}$

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Final Answer:-

$\huge\mathtt {1 + 8\sqrt {3}}$