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Property 5

Simplify: 2...

Question

Simplify:
$\frac{20}{\sqrt{3} - \sqrt{- 2}} + \frac{30}{3 \sqrt{- 2} - 2 \sqrt{3}} - \frac{14}{2 \sqrt{3} - \sqrt{- 2}}$

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Solution

$\frac{20}{\sqrt{3} - \sqrt{- 2}} + \frac{30}{3 \sqrt{- 2} - 2 \sqrt{3}} - \frac{14}{2 \sqrt{3} - \sqrt{- 2}}$

$= \frac{20 (\sqrt{3} + \sqrt{- 2})}{3 + 2} + \frac{30 (3 \sqrt{- 2} + 2 \sqrt{3})}{- 18 - 12} - \frac{14 (2 \sqrt{3} + \sqrt{- 2})}{12 + 2}$

$= \frac{20 (\sqrt{3} + \sqrt{- 2})}{5} + \frac{30 (3 \sqrt{- 2} + 2 \sqrt{3})}{- 30} - \frac{14 (2 \sqrt{3} + \sqrt{- 2})}{14}$

$\Rightarrow 4 (\sqrt{3} + \sqrt{2}) - 3 \sqrt{- 2} - 2 \sqrt{3} - 2 \sqrt{3} - \sqrt{- 2}$

$= 4 \sqrt{3} + 4 \sqrt{- 2} - 3 \sqrt{- 2} - 2 \sqrt{3} - 2 \sqrt{3} - \sqrt{- 2}$

$= 0$

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Q. If a complex number then |z| would be

z = \frac{20}{\sqrt{3} - \sqrt{- 2}} + \frac{30}{3 \sqrt{- 2} - 2 \sqrt{3}} - \frac{14}{2 \sqrt{3} - \sqrt{- 2}}

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