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Math Help - Need to find a domain, cannot factor.

  1. #1
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    Need to find a domain, cannot factor.

    Hey guys. I have the following problem. I am supposed to find the domain of the following function:

    g(x) = \frac{1}{x^2 + 4} - \frac{1}{x^2 - 4}

    This means I'll need to factor the denominators to see what must be excluded from the domain:

    x^2 + 4

    and

    x^2 - 4

    I was able to factor x^2 - 4 easily enough and got:

    (x+2) (x-2)

    Which will exclude 2 and -2 from the domain. I'm lost on how to factor x^2 + 4.

    Help!

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  2. #2
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    Quote Originally Posted by JennyFlowers View Post
    Hey guys. I have the following problem. I am supposed to find the domain of the following function:

    g(x) = \frac{1}{x^2 + 4} - \frac{1}{x^2 - 4}

    This means I'll need to factor the denominators to see what must be excluded from the domain:

    x^2 + 4

    and

    x^2 - 4

    I was able to factor x^2 - 4 easily enough and got:

    (x+2) (x-2)

    Which will exclude 2 and -2 from the domain. I'm lost on how to factor x^2 + 4.

    Help!

    x^2+4 does not factor over the real numbers.

    you found the domain ... all reals except x = \pm 2.

    you're done.
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  3. #3
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    x^2+ 4 does not factor over the real numbers, therefore it is never equal to 0, since, if a polynomial is equal to 0 at x= a, it has (x- a) as a factor.
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