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July 28th, 2013, 08:49 AM  #1 
Senior Member Joined: Aug 2011 Posts: 149 Thanks: 0  Can anyone tell what algebraic formula/trick is used here? Could anyone tell me stepbystep how to get from left to right? I tried to use formula (ab)(ab) but didn't get far with it. Could anyone tell me where and 1+x^2 come from? Rest I can understand. 
July 28th, 2013, 09:08 AM  #2 
Senior Member Joined: Jun 2013 From: London, England Posts: 1,316 Thanks: 116  Re: Can anyone tell what algebraic formula/trick is used her
The trick is to simplify 1  [(1  x^2)/(1 + x^2)]^2 by making 1 = [(1 + x^2)/(1 + x^2)]^2, to get a common denominator. That is a common trick. I1 + x^2I makes no sense as 1 + x^2 is positive in any case. It's not wrong. It's just unnecessary. 
July 28th, 2013, 09:17 AM  #3 
Senior Member Joined: Aug 2011 Posts: 149 Thanks: 0  Re: Can anyone tell what algebraic formula/trick is used her
Thanks. I tried it: Is this right? And how do I use that 0? 
July 28th, 2013, 09:46 AM  #4 
Senior Member Joined: Jun 2013 From: London, England Posts: 1,316 Thanks: 116  Re: Can anyone tell what algebraic formula/trick is used her
The general trick is: 1  a/b = b/b  a/b = (ba)/b Writing 1 as b/b, you get b as a common denominator. In your case, the demominator b = (1 + x^2)^2. You misread my original post. 
July 28th, 2013, 09:52 AM  #5 
Senior Member Joined: Aug 2011 Posts: 149 Thanks: 0  Re: Can anyone tell what algebraic formula/trick is used her
Edit: Thanks, got sqrt(2x^2) now, but where does that 1+x^2 come from? Do I just copy that common denominator to numerator and it's between  and  because it's under sqrt??

July 29th, 2013, 04:50 AM  #6 
Senior Member Joined: Mar 2012 From: Belgium Posts: 654 Thanks: 11  Re: Can anyone tell what algebraic formula/trick is used her
The 1+x^2 has really no use because 1+x^2 is always positive anyway. you can leave it away if you want.

July 29th, 2013, 12:38 PM  #7  
Senior Member Joined: Jul 2013 From: United Kingdom Posts: 471 Thanks: 40  Re: Can anyone tell what algebraic formula/trick is used her Quote:
it's probably another dumb text book question.  
July 30th, 2013, 01:05 AM  #8 
Senior Member Joined: Aug 2011 Posts: 149 Thanks: 0  Re: Can anyone tell what algebraic formula/trick is used her
My question was not that much about  and . It was more abut how am I supposed to know that I have to write (1+x^2) in numerator.

July 30th, 2013, 03:03 AM  #9 
Newbie Joined: Jul 2013 From: Kathmandu, Nepal Posts: 1 Thanks: 0  Re: Can anyone tell what algebraic formula/trick is used her 

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