Question

Please help me solve this with steps
Rationalize the denominator of the following
5+ √3 / 2+ √5

Answer 1

Answer:

$\frac{5 + \sqrt{3} }{2 + \sqrt{5} } = \frac{5 + \sqrt{3} }{2 + \sqrt{5} } \times \frac{2 - \sqrt{5} }{2 - \sqrt{5} } \\ = \frac{2(5 + \sqrt{3} ) - \sqrt{5} (5 + \sqrt{3} )}{2 {}^{2} - ( \sqrt{5 {}^{} ) {}^{2} } } \\ = \frac{10 + 2 \sqrt{3} - 5 \sqrt{5} - \sqrt{15} }{4 - 5} \\ = 10 + 2 \sqrt{3} - 5 \sqrt{5} - \sqrt{15}$