Question

√7-√5/√7+√5 simplify by rationalizing factor

Answer 1

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$= > \: \: \frac{ \sqrt{7} - \sqrt{5} }{ \sqrt{7} + \sqrt{5} } \\ \\ = \frac{( \sqrt{7} - \sqrt{5})( \sqrt{7} - \sqrt{5} ) }{( \sqrt{7} + \sqrt{5} )( \sqrt{7} - \sqrt{5}) } \\ \\ = \frac{ {( \sqrt{7} - \sqrt{5} ) }^{2} }{ {( \sqrt{7} )}^{2} - {( \sqrt{5} )}^{2} } \\ \\ = \frac{7 + 5 - 2 \sqrt{7 \times 5} }{7 - 5} \\ \\ = \frac{12 - 2 \sqrt{35} }{2} = \frac{2(6 - \sqrt{35}) }{2} \\ \\ = 6 - \sqrt{35}$
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