SOLUTION: Alrighty, here is the question, 6 _____ 3+ sqrt 5 , I know that you have to use the conjugates when the same # with the different sign in the mid

Question 97111This question is from textbook precalculus graphs and models
: Alrighty, here is the question,
6
_____
3+ sqrt 5 , I know that you have to use the conjugates when the same # with the different sign in the middle, so it should then look like this
6 3-sqrt5 18 +6sqrt 5
__________*______ =
3+sqrt 5 3-sqrt 5
then I think you foil the denominator, and get (3+sqrt5)(3-sqrt5), and this = to 9+3-sqrt5+3+sqrt5, and sqrt -5 and sqrt 5=-25, =-5and the middle cancels out and leaves you with 9-5=4 but the answer in the back of book is 9-3sqrt5
_______
2
how did they get that? thank you for your time. Stacy
_____ This question is from textbook precalculus graphs and models

Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
I'm assuming you want to rationalize the denominator right?

Start with the given expression

Multiply the fraction by

Combine the fractions

Foil

Combine and cancel out like terms

Multiply

Combine like terms

Reduce to (this is probably where you got lost. You should have reduced before you distributed.)

Distribute

Check:

Plug in the expression into your calculator to approximately get 1.14589803375031

Now plug in into your calculator to approximately get 1.14589803375031

Since they are equivalent, (ie ) this verifies our answer
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