Question

Rationalize the denominator of
5/(6 + 3sqrt2) - (2 + 2sqrt2)

Answer 1

I'm assuming everything after / is in the denominator, so first let's simplify it a little.

Answer 2

yes

Answer 3

To simplify it just expand the parenthesis and do some algebra to get:
6-2+3sqrt(2)-2sqrt(2) = 4 +sqrt(2)

Answer 4

So now our fraction is just
5/(4+sqrt(2))
Do you know what rationalization does to a fraction?

Answer 5

..no :/

Answer 6

It gets rid of all the roots in the denominator. So how would you get rid of sqrt(2) in 4+sqrt(2)?

Answer 7

I should say how would you get rid of the sqrt in 4+sqrt(2)?

Answer 8

Hint:
c/(a+b) = c*(a-b)/( (a+b)(a-b) )

Answer 9

You have:
5/(4+sqrt(2))