Question

Rationaline the denominater and
Simplify​

Answer 1

Answer:

$\frac{ \sqrt{5} + \sqrt{3} }{ \sqrt{5} - \sqrt{3 }} + \frac{ \sqrt{5} - \sqrt{3} }{ \sqrt{5} + \sqrt{3} } = 8$

Step-by-step explanation:

$\frac{ \sqrt{5} + \sqrt{3} }{ \sqrt{5} - \sqrt{3 }} + \frac{ \sqrt{5} - \sqrt{3} }{ \sqrt{5} + \sqrt{3} } \\ = \frac{ \sqrt{5} + \sqrt{3} }{ \sqrt{5} - \sqrt{3} } \times \frac{ \sqrt{5} + \sqrt{3} }{ \sqrt{5} + \sqrt{3} } + \frac{ \sqrt{5} - \sqrt{3} }{ \sqrt{5} + \sqrt{3} } \times \frac{ \sqrt{5} - \sqrt{3} }{ \sqrt{5} - \sqrt{3} } \\ = \frac{ {( \sqrt{5} + \sqrt{3} )}^{2} }{ {( \sqrt{5}) }^{2} - { (\sqrt{3}) }^{2} } + \frac{ {( \sqrt{5} - \sqrt{3} )}^{2} }{ {( \sqrt{5}) }^{2} - { (\sqrt{3}) }^{2} } \\ = \frac{ {( \sqrt{5} )}^{2} + {( \sqrt{3} )}^{2} + 2( \sqrt{5})( \sqrt{3}) }{5 - 3} + \frac{ {( \sqrt{5} )}^{2} + {( \sqrt{3} )}^{2} - 2( \sqrt{5})( \sqrt{3}) }{5 - 3} \\ = \frac{5 + 3 + 2 \sqrt{15} }{5 - 3} + \frac{5 + 3 - 2 \sqrt{15} }{5 - 3} \\ = \frac{8 + 2 \sqrt{15} }{2} + \frac{8 - 2 \sqrt{15} }{2} \\ = \frac{8 + 2 \sqrt{15} + 8 - 2 \sqrt{15} }{2} \\ = \frac{8 + 8 + 2 \sqrt{15 } - 2 \sqrt{15} }{2} \\ = \frac{16}{2} \\ = 8$