SOLUTION: Hi. My question is how do I write the following in simplified radical form by rationalizing the denominator? 2sqrt2+1 ________ -5sqrt2+3 I've been at it for 2 hours.

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Question 248888: Hi. My question is how do I write the following in simplified radical form by rationalizing the denominator?
2sqrt2+1
________
-5sqrt2+3
I've been at it for 2 hours. I've tried using the conjugate but it's confusing because it seems to be written in a different form than the textbook. I've gotten 2 different answers, the latest one being:
-3-21sqrt2
__________

41
I'm not sure if I doing this right. If someone could help me, it would be greatly appreciated. Thank you.

Answer by Theo(13342)   (Show Source): You can put this solution on YOUR website!
your equation is:



the conjugate of the denominator would be

multiply the expression by to get:



perform the indicated operations to get:



you got the denominator ok.

you got pieces of the numerator ok but something went wrong somewhere.

the numerator became:



multiplying these terms together you would get:






combining like terms you would get

your answer is .




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