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(1+x)^2/x^6 doesn't simplify?

  1. Nov 2, 2005 #1

    Pengwuino

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    Gold Member

    Ok I got an equation here...
    [tex]2\sqrt {\frac{{(1 + 2t^4 )^2 }}{{t^6 }}}[/tex]
    is the equation (sorry for misleading title but its the same concept).
    Now I was always under the assumption that the top square could be removed as long as you reduce the bottom to [tex]t^3[/tex] since [tex]t^3[/tex] squared is [tex]t^6[/tex] and that you can cancel out squares like that. I guess I'm wrong? I'm running some examples in my mind and I'm kinda realizing you can't do it... but i feel like ive always thought it was true for soem reason.
    I also did a simplification through mathematica and found out that the square root actually allows you to remove the [tex]^3[/tex] to get to the [tex]t^3[/tex].
    The first question i'm asking is: without that square root... would I be able to simplify?
    The 2nd question is exactly why I am able to use that square root to simplify. Sorry if its confusing....
     
    Last edited: Nov 2, 2005
  2. jcsd
  3. Nov 2, 2005 #2

    TD

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    Homework Helper

    Well you can get rid off the square root, since

    [tex]
    \sqrt {\frac{{a^2 }}
    {{b^2 }}} = \sqrt {\left( {\frac{a}
    {b}} \right)^2 } = \left| {\frac{a}
    {b}} \right|[/tex]
     
  4. Nov 2, 2005 #3

    Pengwuino

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    Gold Member

    Yah I was under the impression that even without that square root, it could turn into a/b
     
  5. Nov 2, 2005 #4
    Just remember that the quantity has to remain positive. So the simplification of the original equation is:
    [tex]
    |{1/t^3 + 2t}|[/tex]
     
  6. Nov 2, 2005 #5
    If you want to see the reduction broken down then this is what you should do.
    [tex] 2\sqrt{\frac{(1+t^4)^2}{t^6}} =2\left(\frac{(1+t^4)^{2\frac{1}{2}}}{t^6}\right)^{\frac{1}{2}}[/tex]
    [tex]=2\frac{(1+t^4)^{2\frac{1}{2}}}{t^{6\frac{1}{2}}}=2\frac{1+t^4}{t^3} [/tex]
    [tex]=2t^{-3}+2t^{-3+4}=|2(t^{-3}+t)| [/tex]

    which almost yields the same result as knavish. I think he is missing a factor of 2 somewhere in there as

    p.s. sorry I didn't break it down with the absolute value signs, but those were already explained pretty well... and for some reason I like to add them afterwards. bad habit i guess
     
    Last edited: Nov 2, 2005
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