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Rationalisation

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Question

Simplify: $\frac{\sqrt{5} + \sqrt{3}}{\sqrt{5} - \sqrt{3}} + \frac{\sqrt{5} - \sqrt{3}}{\sqrt{5} + \sqrt{3}}$

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Solution

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

= $\frac{5 + 3 + 2 \sqrt{15} + 5 + 3 - 2 \sqrt{15}}{5 - 3} = \frac{16}{2} = 8$

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Similar questions

\frac{3 + \sqrt{5}}{3 - \sqrt{5}} + \frac{3 - \sqrt{5}}{3 + \sqrt{5}}

\frac{\sqrt{5} - \sqrt{3}}{\sqrt{5} + \sqrt{3}} + \frac{\sqrt{5} + \sqrt{3}}{\sqrt{5} - \sqrt{3}}

Q. Simplify the following:

\frac{\sqrt{5} + \sqrt{3}}{\sqrt{5} - \sqrt{3}} + \frac{\sqrt{5} - \sqrt{3}}{\sqrt{5} + \sqrt{3}}

(- 3 + \sqrt{5}) (- 3 - \sqrt{5})

(3 \sqrt{5} - 5 \sqrt{2}) (4 \sqrt{5} + 3 \sqrt{2})

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