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Topic: Please help me simplify this expression.
Replies: 5   Last Post: Jan 24, 2005 2:20 AM

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George Cox

Posts: 868
Registered: 12/6/04
Re: Please help me simplify this expression.
Posted: Jan 24, 2005 2:19 AM
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aaronhunter@gmail.com wrote:
>
> Hello. I have the following expression. I have got it figured out
> except I am missing a minor detail that is causing me to have 2x+1
> instead of 2(x+1) in my final numerator. Please help!
>
> Note that x^1 is (x to the first power) ^-(1/2) is to the negative 1/2
> power etc...
>
> Problem: [x(x+2)^-(1/2) + (x+2)^(1/2) ] / (x+2)^(3/2)
>
> I first separate out the problem and combine the lower exponents to get
> [x((2/(x+2)) + 1/(x+2)] / (x+2)


Well that's wrong! I'm not sure what "combine the lower exponents"
means but I'd proceed as follows. You have

x(x + 2)^{-1/2} + (x + 2)^{1/2}
-------------------------------
(x + 2)^{3/2}

multiply top and bottom by (x + 2)^{1/2} to get

x + (x + 2)
-----------
(x + 2)^2

or

2(x + 1)
---------
(x + 2)^2
>
> ...
> What step am I missing to get quantity 2(x+1) / (x+2)^2???


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