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Addition and Subtraction of Like and Unlike Surds

Solve: 2 + √...

Question

Solve:
$\frac{2 + \sqrt{3}}{2 - \sqrt{3}} + \frac{2 - \sqrt{3}}{2 + \sqrt{3}} + \frac{\sqrt{3} - 1}{\sqrt{3} + 1}$

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Solution

$\frac{2 + \sqrt{3}}{2 - \sqrt{3}} + \frac{2 - \sqrt{3}}{2 + \sqrt{3}} + \frac{\sqrt{3} - 1}{\sqrt{3} + 1}$

$\frac{{(2 + \sqrt{3})}^{2} + {(2 - \sqrt{3})}^{2}}{(2 - \sqrt{3}) (2 + \sqrt{3})} + \frac{\sqrt{3} - 1}{\sqrt{3} + 1} \times \frac{\sqrt{3} - 1}{\sqrt{3} + 1}$

$\frac{4 + 3 + 4 \sqrt{3} + 4 + 3 - 4 \sqrt{3}}{1} + \frac{3 + 1 - 2 \sqrt{3}}{2}$

$14 + 2 - \sqrt{3}$

$16 - \sqrt{3}$

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