Question

How to solve this problem

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Answer 1

Given :

• Simplify :

$\bf\frac{2\sqrt{6} }{\sqrt{2} + \sqrt{3} } + \frac{6\sqrt{2} }{\sqrt{6} +\sqrt{3} } - \frac{8\sqrt{3} }{\sqrt{6} +\sqrt{2} }$

Solution :

Rationalize the denominator

⠀⠀⠀⠀ ⠀ ⠀⠀ ⠀⠀⠀

$:\implies\tt\frac{2\sqrt{6} }{\sqrt{2} + \sqrt{3} } + \frac{6\sqrt{2} }{\sqrt{6} +\sqrt{3} } - \frac{8\sqrt{3} }{\sqrt{6} +\sqrt{2} }$

$:\implies\tt\frac{2 \sqrt{6} }{ \sqrt{2} + \sqrt{3} } \times \frac{1}{ \sqrt{2} - \sqrt{3} } + \frac{6 \sqrt{2} }{ \sqrt{6} + \sqrt{3} } \times \frac{1}{ \sqrt{6} - \sqrt{3} } - \frac{8 \sqrt{3} }{ \sqrt{6} + \sqrt{2} } \times \frac{1}{ \sqrt{6} - \sqrt{2} }$

$:\implies\tt \frac{2 \sqrt{6} }{( \sqrt{2}) ^{2} - {( \sqrt{3} })^{2} } + \frac{6 \sqrt{2} }{ {( \sqrt{6}) }^{2} - { (\sqrt{3} })^{2} } - \frac{8 \sqrt{3} }{ { (\sqrt{6} )}^{2} - { (\sqrt{2} })^{2} }$

$:\implies\tt\: 2 \sqrt{6} \times ( \sqrt{3} - \sqrt{2} ) + 2 \sqrt{2} \times ( \sqrt{6} - \sqrt{3} ) - 2 \sqrt{3} \times \sqrt{6} - \sqrt{2}$

$:\implies\tt\:2 \times \sqrt{18} - 2 \sqrt{12} + 2 \times \sqrt{12} - 2 \sqrt{6} - 2 \times \sqrt{18} + 2 \times \sqrt{6}$

$:\implies\tt\: ( 2 × \sqrt{18} - 2 ×\sqrt{18}) + (2 ×\sqrt{12} - 2 × \sqrt{12}) + (2 × \sqrt{16} - 2 × \sqrt{16})$

$:\implies\tt\: 0 + 0 + 0$

$:\implies\tt\: 0$

Answer 2

Answer:

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