Verified answer

(√6 + √3) / (√3 - √6) times (√3 + √6) /(√3 + √6)

√36 +2√18 +√9 all over √9-√36

6 +6√3 +3 all over 3-6

9 + 6 √3 all over -3

-3 -2√3

Ok so for this problem, you want to get rid of the radicals in the denominator. To do this, multiply both the numerator and the denominator by (sqrt 6 + sqrt 3). The reason is that when you multiply a radical by itself, the answer is a regular number. Since the denominator is (sqrt 6 MINUS sqrt 3), you multiply both parts of the fraction by (sqrt 6 PLUS sqrt 3)**** (if you still dont get this, go to the very bottom of the response)**

So, when you do this, you should get

(sqrt 6 +sqrt 3)(sqrt 6+sqrt 3)

_____________________________

(sqrt 3-sqrt 6) (sqrt 3+sqrt 6)

which simplifies down to..

6+6+3

______

3-6

This is 15/(-3) when you simplify, which is -5.

Hope this helped!!!!

*** Ok so when i was saying that you multiply (sqrt 3-sqrt 6) by (sqrt 3+sqrt6), it confuses a lot of people, so i'll use simpler examples to explain.

ex. (x+3) (x+3) = x^2 +6x +9 When the operation is the same

(x+3) (x-3) = x^2-9 When the operations are different

See how much easier the second one was?? This is what I applied to above.

(√6 + √3) / (√3 - √6)

Times top and bottom by (√3 +√6) so that you get different of two squares on bottom, so if you work it all it you get,

15/ -3

= - 5