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July 28th, 2013, 08:49 AM   #1
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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.
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July 28th, 2013, 09:08 AM   #2
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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.
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July 28th, 2013, 09:17 AM   #3
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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?
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July 28th, 2013, 09:46 AM   #4
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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.
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July 28th, 2013, 09:52 AM   #5
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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??
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July 29th, 2013, 04:50 AM   #6
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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.
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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.
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July 30th, 2013, 01:05 AM   #8
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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.
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July 30th, 2013, 03:03 AM   #9
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Re: Can anyone tell what algebraic formula/trick is used her

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