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Math Help - [SOLVED] Finding the Domain of a quadratic

  1. #1
    Barret52
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    [SOLVED] Finding the Domain of a quadratic

    I am having trouble finding the domain of

    x^3 + 5x
    ------------
    x^2 - 6x + 8


    Thanks for your Help
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  2. #2
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by Barret52 View Post
    I am having trouble finding the domain of

    x^3 + 5x
    ------------
    x^2 - 6x + 8


    Thanks for your Help
    Limitations on the domain of a function take the form of zeros in the denominator, negative numbers under a square root sign, and the like. Here we have a fraction so we want to look at where the denominator goes to zero.

    x^2 - 6x + 8 = (x - 4)(x - 2) = 0

    So the denominator is zero at x = 2 and x = 4. Thus these values for x cannot be in the domain. This is our only restriction, so the domain will be:
    ( -\infty, 2) \cup (2, 4) \cup (4, \infty)

    or, more simply, "all real x except 2 and 4."

    -Dan
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