Question

Simplify
7+3√5/3+√5- 7-2√5/3-√5

Answer 1

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$\huge\underline\mathfrak\green{solution:-}$

$\red\longrightarrow\tt \frac{7 + 3 \sqrt{5} }{3 + \sqrt{5} } - \frac{7 - 2 \sqrt{5} }{3 - \sqrt{5} }$

$\red\longrightarrow \tt \frac{(7 + 3 \sqrt{5})(3 - \sqrt{5}) - (3 + \sqrt{5})(7 - 2 \sqrt{5} ) }{(3 + \sqrt{5})(3 - \sqrt{5} ) }$

$\red\longrightarrow \tt\frac{(21 - 7 \sqrt{5} + 9 \sqrt{5} - 3 \times 5) - (21 - 6 \sqrt{5} + 7 \sqrt{5} - 2 \times 5)}{ {3}^{2} - { (\sqrt{5} )}^{2} }$

$\red\longrightarrow \tt \frac{21 + 2 \sqrt{5} - 15 - 21 - \sqrt{5} + 10 }{9 - 5}$

$\red\longrightarrow \tt\frac{ \sqrt{5 } - 5 }{4}$

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