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Remove irrationality from these fractions


How to remove irrationality from these fractions: a) [tex]\frac{2}{3\sqrt{3}}[/tex] b) [tex]\frac{2}{2-\sqrt{3}}[/tex] c) [tex]\frac{1}{\sqrt{5}+\sqrt{3}}[/tex] ?

Last time edited 2019-01-25

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a) [tex]\frac{2}{3\sqrt{3}}=\frac{2}{3\sqrt{3}}\cdot \frac{\sqrt{3}}{\sqrt{3}}=\frac{2\sqrt{3}}{\large{9}}[/tex]

Last time edited 2019-01-20

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b) [tex]\frac{2}{2-\sqrt{3}}=\frac{2}{2-\sqrt{3}}\cdot \frac{2+\sqrt{3}}{2+\sqrt{3}}=\frac{2(2+\sqrt{3})}{2^2-\sqrt{3^2}}={2(2+\sqrt{3})}[/tex]

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c) [tex]\frac{1}{\sqrt{5}+\sqrt{3}}=\frac{1}{\sqrt{5}+\sqrt{3}}\cdot \frac{\sqrt{5}-\sqrt{3}}{\sqrt{5}-\sqrt{3}}=\frac{\sqrt{5}-\sqrt{3}}{\large{2}}[/tex]

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