Question

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Answer 1

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

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