Question

Which of the following is equivalent to -12/(√13-√6)
answer it please i have exam today

Answer 1

$\frac{ - 12}{ \sqrt{13} - \sqrt{6} }$

See rationalising factor of √a - √b is √a + √b

Thus rationalising factor of √13 - √6 is √13 + √6

So we have

$\frac{( - 12)}{ (\sqrt{13} - \sqrt{6}) } \times \frac{ (\sqrt{13} + \sqrt{6} ) }{ (\sqrt{13} + \sqrt{6}) }$

Thus

$\frac{ - 12( \sqrt{13} + \sqrt{6}) }{( \sqrt{13} - \sqrt{6})( \sqrt{13} + \sqrt{6}) }$

$\frac{ - 12( \sqrt{13} + \sqrt{6} ) }{ { (\sqrt{13}) }^{2} - { (\sqrt{6} )}^{2} }$

$\frac{ - 12( \sqrt{13} + \sqrt{6}) }{13 - 6}$

$\frac{ - 12( \sqrt{13} + \sqrt{6} )}{7}$

This is required answer

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Answer 2

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