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Math Help - Factoring problem with negative and rational exponents

  1. #1
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    Factoring problem with negative and rational exponents

    I just can't seem to get this one, it's in the first assignment of my semester...

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

    thanks for any hel;p, i just want to know how to do it not even the answer necessarily
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  2. #2
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    x^(-1/2)(3x+4)^(1/2)+3x^(1/2)(3x+4)^(-1/2)

    should be written like this sorry
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  3. #3
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    Quote Originally Posted by jorygoldsmith View Post
    x^(-1/2)(3x+4)^(1/2)+3x^(1/2)(3x+4)^(-1/2)

    should be written like this sorry
    x^{-1/2}(3x+4)^{1/2} + 3x^{1/2}(3x+4)^{-1/2}

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

    [x(3x+4)]^{-1/2}(6x+4)

    \displaystyle \frac{2(3x+2)}{\sqrt{x(3x+4)}}
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  4. #4
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    how about

    [(x+h)^(-2)-(x)^(-2)]/h
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  5. #5
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    easier this way ...

    \displaystyle \frac{1}{h} \left[\frac{1}{(x+h)^2} - \frac{1}{x^2}\right]

    get a common denominator and combine the two fractions inside the [brackets], then combine like terms and factor the numerator ... ultimate goal is to get the "h" in the first fraction to cancel.


    also ... next time, start a new problem w/ a new thread.
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