Question

please help me to solve this question.​

Answer 1

$\frac{1}{ \sqrt{5} + \sqrt{3} } \times \frac{ \sqrt{5} - \sqrt{3} }{ \sqrt{5 } - \sqrt{3} } \\ \\ = > \frac{ \sqrt{5} - \sqrt{3} }{ ({ \sqrt{5}) }^{2} - {( \sqrt{3} )}^{2} } \\ \\ = > \frac{ \sqrt{5} - \sqrt{3} }{5 - 3} \\ \\ = \frac{ \sqrt{5} - \sqrt{3} }{2}$

Note : For rationalising, you just have to multiply the given expression by its conjugate (most of the time).

Hope this helps!