Question

Rationalise the denominator of:
$\frac{5}{ \sqrt{3}- \sqrt{5} }$
plz don't give silly answers​

Answer 1

Answer:

$- \dfrac{5 \sqrt{3} + 5 \sqrt{5} }{2}$

Step-by-step explanation:

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