Question

Rationalize the denominator


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Answer 1

Answer:

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

Step-by-step explanation:

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

Answer 2

$\begin{gathered}\frac{3}{(\sqrt{3}+\sqrt{5}) - 2\sqrt{3}} = \frac{3}{\sqrt{5} - \sqrt{3}} \\ =\frac{3}{\sqrt{5} - \sqrt{3}} * \frac{{\sqrt{5} + \sqrt{3}}}{{\sqrt{5} + \sqrt{3}}} \\ = \frac{3({\sqrt{5} + \sqrt{3}})}{\sqrt{5} ^{2} - \sqrt{3} ^{2}} \\ =\frac{3({\sqrt{5} + \sqrt{3}})}{5-3} = \frac{3({\sqrt{5} + \sqrt{3}})}{2}\end{gathered}$