Question 64287
To simplify:  (5)/(9-sqrt(3))

First, we want to get rid of the radical in the denominator.  We do this by multiplying the factor (9-sqrt(3)) by its conjugate (9+sqrt(3)). when we do this we get:
(5)/(81-9sqrt3+9sqrt3-3) or

(5)/(81-3) simplifying, we have:

5/78

Note:  If the original factor is (a+b), the conjugate of (a+b) is defined as the factor that, when multiplied by the original factor, yields the answer (a^2-b^2) and that factor is (a-b)--a powerful tool for simplifying radicals and complex numbers.

Hope this helps.  Have a nice holiday season---ptaylor