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Math Help - rational exponents for factoring

  1. #1
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    rational exponents for factoring

    i am having pre cal woes

    today was the first day of school and i cant remember how to do this home work


    3/4(x^2+1)^(-1/4)-(1/2)(x^2+1)^(3/4)

    step by step would be awesome
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by rohizzle121 View Post
    i am having pre cal woes

    today was the first day of school and i cant remember how to do this home work


    3/4(x^2+1)^{-1/4}-(1/2)(x^2+1)^{3/4}

    step by step would be awesome
    the common term is x^2 + 1, start by factoring out the lowest power of it (you can also factor out a 1/4 to make things look nice, but lets keep things simple.

    so you get (x^2 + 1)^{-1/4}( \cdots

    can you finish?
    Last edited by Jhevon; August 25th 2008 at 03:16 PM.
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  3. #3
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    Quote Originally Posted by Jhevon View Post
    the common term is x^2 + 1, start by factoring out the lowest power of it (you can also factor out a 4 to make things look nice, but lets keep things simple.

    so you get (x^2 + 1)^{-1/4}( \cdots

    can you finish?
    when i try that i get
    (x^2 + 1)^{-1/4}({3/4}-{1/2}^{1/2})


    i am like 100% i did somthing wrong

    after i take the common i am not sure what to do with the rest
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  4. #4
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by rohizzle121 View Post
    when i try that i get
    (x^2 + 1)^{-1/4}({3/4}-{1/2}^{1/2})


    i am like 100% i did somthing wrong

    after i take the common i am not sure what to do with the rest
    indeed, you did do something wrong. if you factor out (x^2 + 1)^{-1/4} from (x^2 + 1)^{3/4} you are left with (x^2 + 1) since (x^2 + 1)^{3/4} = (x^2 + 1)(x^2 + 1)^{-1/4}

    you have to make sure that when you factor something out, that the powers of the base add up to the original power
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    Quote Originally Posted by Jhevon View Post
    indeed, you did do something wrong. if you factor out (x^2 + 1)^{-1/4} from (x^2 + 1)^{3/4} you are left with (x^2 + 1) since (x^2 + 1)^{3/4} = (x^2 + 1)(x^2 + 1)^{-1/4}

    you have to make sure that when you factor something out, that the powers of the base add up to the original power

    i am still quite confused
    {3/4}(x^2+1)^{-1/4}-{1/2}(x^2+1)^{3/4}
    would then lead to

    (x^2+1)^{-1/4}-{1/2}(x^2+1)
    then
    i am completely lost
    i plan on going tomorrow for tutorials after school i just want to try right now
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  6. #6
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by rohizzle121 View Post
    i am still quite confused
    {3/4}(x^2+1)^{-1/4}-{1/2}(x^2+1)^{3/4}
    would then lead to

    (x^2+1)^{-1/4}-{1/2}(x^2+1)
    then
    i am completely lost
    i plan on going tomorrow for tutorials after school i just want to try right now
    \frac 34(x^2 + 1)^{-1/4} - \frac 12 (x^2 + 1)^{3/4} = (x^2 + 1)^{-1/4} \bigg( \frac 34 - \frac 12 (x^2 + 1) \bigg) ........note that if you multiply this out, you get back the original. this was not true with what you wrote.

    to make it look nicer, we can factor out a 1/4, to get:

    \frac 14 (x^2 + 1)^{-1/4} [3 - 2(x^2 + 1)] = \frac 14 (x^2 + 1)^{-1/4}(1 - 2x^2) = \frac 14 (1 - 2x^2)(x^2 + 1)^{-1/4}


    look carefully at what i did. now's your chance to ask questions
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  7. #7
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    Quote Originally Posted by Jhevon View Post
    indeed, you did do something wrong. if you factor out (x^2 + 1)^{-1/4} from (x^2 + 1)^{3/4} you are left with (x^2 + 1) since (x^2 + 1)^{3/4} = (x^2 + 1)(x^2 + 1)^{-1/4}

    you have to make sure that when you factor something out, that the powers of the base add up to the original power
    i understand up to that part why is this true (x^2 + 1)^{3/4} = (x^2 + 1)(x^2 + 1)^{-1/4}

    and on the second part after you took out the 1/4 i am totally confused
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  8. #8
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by rohizzle121 View Post
    i understand up to that part why is this true (x^2 + 1)^{3/4} = (x^2 + 1)(x^2 + 1)^{-1/4}

    and on the second part after you took out the 1/4 i am totally confused
    forget factoring out the 1/4. did you get up to the step before that?
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