http://i.imgur.com/psqwL.gif

I can't seem to solve this one. I tried reversing the signs, which didn't work for me. How do I solve this one?

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- Sep 2nd 2012, 11:58 AMDiesalRationalize the Denominator
http://i.imgur.com/psqwL.gif

I can't seem to solve this one. I tried reversing the signs, which didn't work for me. How do I solve this one? - Sep 2nd 2012, 12:08 PMPlatoRe: Rationalize the Denominator
- Sep 2nd 2012, 01:00 PMDevenoRe: Rationalize the Denominator
that won't quite do the job.

$\displaystyle (1 + \sqrt{3} - \sqrt{5})(1 - \sqrt{3} + \sqrt{5}) = 1^2 - (\sqrt{3} - \sqrt{5})^2 $

$\displaystyle = 1 - (3 - 2\sqrt{15} + 5) = -7 + 2\sqrt{15}$, which certainly isn't rational.

i propose instead multiplying top and bottom by:

$\displaystyle 7 + 3\sqrt{3} + \sqrt{5} + 2\sqrt{15}$, since:

$\displaystyle (1 + \sqrt{3} - \sqrt{5})(7 + 3\sqrt{3} + \sqrt{5} + 2\sqrt{15}) = 11$ - Sep 2nd 2012, 01:07 PMPlatoRe: Rationalize the Denominator
You are correct. I entered is incorrectly into my CAS.

- Sep 2nd 2012, 07:51 PMProve ItRe: Rationalize the Denominator