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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 step-by-step how to get from left to right? I tried to use formula (a-b)(a-b) 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 = (b-a)/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
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Re: Can anyone tell what algebraic formula/trick is used her

Quote:
 Originally Posted by Pero 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.
would say so too. why would someone leave the modulus there. since this is the case, (1+x^2) is exactly the same as |1+x^2|

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  Tags algebraic, formula or trick Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post demipaul Abstract Algebra 1 October 1st, 2009 05:08 PM demipaul Algebra 5 October 1st, 2009 10:15 AM realritybugll Calculus 5 August 28th, 2009 10:18 PM SANSRICE Algebra 7 March 23rd, 2009 10:56 AM stainburg Calculus 1 December 31st, 1969 04:00 PM

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