Question

14. Simplify:
$( \frac{ \sqrt{5 - 1} }{ \sqrt{5 + 1} } + \frac{ \sqrt{5 + 1} }{ \sqrt{5 - 1} }$
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Answer 1

Question:-

Simplify:

$\frac{ \sqrt{5 - 1} }{ \sqrt{5 + 1} } + \frac{ \sqrt{5 + 1} }{ \sqrt{5 - 1} }$

Solution:-

We have,

$\sqrt{5 - 1} = \sqrt{4} = 2$

$\sqrt{5 + 1} = \sqrt{6}$

Substitute

= $\frac{2}{ \sqrt{6} } + \frac{ \sqrt{6} }{2}$

= $\frac{(2 \times 2) + (\sqrt{6} \times \sqrt{6}) }{2 \sqrt{6} }$

= $\frac{4 + 6}{2 \sqrt{6} }$

= $\frac{10}{2 \sqrt{6} }$

= $\frac{5}{ \sqrt{6} } \: \: (or) \: \: \frac{5}{ \sqrt{5 + 1} }$