Question

Rationalize the denominator ​

Answer 1

Answer:

1)

a)-3√6-3√7

b) (√7-√2)/5

Step-by-step explanation:

a)

$\frac{3}{ \sqrt{6} - \sqrt{7} } \\ = \frac{3( \sqrt{6} + \sqrt{7}) }{ \sqrt{6} - \sqrt{7} ( \sqrt{6} + \sqrt{7}) } \\ = \frac{3 \sqrt{6} + 3 \sqrt{7} }{6 - 7 } \\ = - 3 \sqrt{6} - 3 \sqrt{7}$

b)

$\frac{1}{ \sqrt{7} + \sqrt{2} } \\ = \frac{1( \sqrt{7} - \sqrt{2} ) }{ \sqrt{7} + \sqrt{2}( \sqrt{7} - \sqrt{2} ) } \\ = \frac{ \sqrt{7} - \sqrt{2} }{7 - 2} \\ = \frac{ \sqrt{7} - \sqrt{2} }{5}$