SOLUTION: The last tutor didn't quite get the same answer that's located in the back of my book. Here is the problem: (sqrt 2)/(1+sqrt 3) I know the answer is as follows. I just don't know

Algebra ->  Square-cubic-other-roots -> SOLUTION: The last tutor didn't quite get the same answer that's located in the back of my book. Here is the problem: (sqrt 2)/(1+sqrt 3) I know the answer is as follows. I just don't know       Log On


   



Question 88422This question is from textbook Mathematics with Applications
: The last tutor didn't quite get the same answer that's located in the back of my book. Here is the problem:
(sqrt 2)/(1+sqrt 3) I know the answer is as follows. I just don't know why.
ANSWER: (-sqrt2 + sqrt6)/(2) Can you help?
This question is from textbook Mathematics with Applications

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Multiply numerator and denominator by (1-sqrt3) to get:
[sqrt2*(1-sqrt3)]/[(1+sqrt3)(1-sqrt3)]
= [sqrt2 - sqrt6]/[1 - 3]
= [sqrt2 - sqrt6]/(-2)
= [-sqrt2+sqrt6]/2
========
Cheers,
Stan H.