Question

simplify √3-√5)(√5+√3)/7-2√5​

Answer 1

Answer:

$= \frac{ (\sqrt{3} - \sqrt{5}) ( \sqrt{3} + \sqrt{5} )}{7 - 2 \sqrt{5} } \\ = \frac{ - 2}{7 - 2 \sqrt{5} } \times \frac{7 + 2 \sqrt{5} }{7 + 2 \sqrt{5} } \\ = \frac{ - 2(7 + 2 \sqrt{5} )}{49 - 20} \\ = \frac{ - 2(7 + 2 \sqrt{5}) }{29} \\ \\ hope \: it \: will \: help \: you.$

Answer 2

$\huge\underline\mathfrak{Answer:}$

We have

$\frac{( \sqrt{3} - \sqrt{5})( \sqrt{5 + \sqrt{3}) } }{7 - 2 \sqrt{5} } = \frac{( \sqrt{3)} {}^{2} - ( \sqrt{5}) {}^{2} }{7 -2 \sqrt{5} } \\ \\ = \frac{3 - 5}{7 - 2 \sqrt{5} } \\ \\ = \frac{2}{7 - 2 \sqrt{5} } \times \frac{7 + \sqrt{5} }{7 + 2 \sqrt{5} } \\ \\ = \frac{ - 2 \times (7 + 2 \sqrt{5}) }{(7) {}^{2} - (2 \sqrt{5}) {}^{2} } \\ \\ = \frac{ - 2(7 + 2 \sqrt{5}) }{49 - 20} \\ \\ = \frac{ - 2(7 + 2 \sqrt{5)} }{29} \\ \\ = \frac{ - 2}{29} (7 + 2 \sqrt{5)}$