Question

$\frac{5 + \sqrt{3} }{7 - 4 \sqrt{3} - \frac{5 - \sqrt{3} }{7 + 4 \sqrt{3} }$
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Answer 1

Answer:

$\frac{5 + \sqrt{3} }{7 - 4 \sqrt{3}} - \frac{5 - \sqrt{3} }{7 + 4 \sqrt{3}} \\ taking \: lcm \\ \frac{(5 + \sqrt{3})(7 + 4 \sqrt{3}) - (5 - \sqrt{3} )(7 - 4 \sqrt{3}) }{(7 - 4 \sqrt{3} )(7 + 4 \sqrt{3} )} \\ \frac{(35 + 20 \sqrt{3} + 7 \sqrt{3} + 12) - (35 - 20 \sqrt{3} - 7 \sqrt{3} + 12 }{49 - 48} \\ = 35 - 35 + 20 \sqrt{3} + 20 \sqrt{3} + 7 \sqrt{3} + 7 \sqrt{3} + 12 - 12 \\ = 54 \sqrt{3}$

Answer....

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