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Math Help - Can't find this limit analytically

  1. #1
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    Can't find this limit analytically

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

    I need to find the limit as x approaches 3. I've simplified it to a number of other forms, but I can't get it into a form where x=3 doesn't equate to an undefined value. I know that the answer is -(1/16). Can anyone help point me in the right direction?
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    Re: Can't find this limit analytically

    Quote Originally Posted by Diogenes View Post
    (((1/(x+1))-(1/4))/(x-3)
    I need to find the limit as x approaches 3. I've simplified it to a number of other forms, but I can't get it into a form where x=3 doesn't equate to an undefined value. I know that the answer is -(1/16). Can anyone help point me in the right direction?
    That fraction reduces to \frac{-1}{4x+4}
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  3. #3
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    Re: Can't find this limit analytically

    Quote Originally Posted by Diogenes View Post
    (((1/(x+1))-(1/4))/(x-3)

    I need to find the limit as x approaches 3. I've simplified it to a number of other forms, but I can't get it into a form where x=3 doesn't equate to an undefined value. I know that the answer is -(1/16). Can anyone help point me in the right direction?
    start by simplifying the complex fraction ...

    \frac{\frac{1}{x+1} - \frac{1}{4}}{x-3} \cdot \frac{4(x+1)}{4(x+1)}
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    Re: Can't find this limit analytically

    Whenever you see a problem like this, try to simplify it to a rational function (quotient of two polynomials, such as \frac{4 - (x+1)}{4(x-3)(x+1)}, using various strategies like common denominators, etc. Then pull out any common factors. (You may need to find the roots.)
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    Re: Can't find this limit analytically

    Quote Originally Posted by Plato View Post
    That fraction reduces to \frac{-1}{4x+4}
    Quote Originally Posted by skeeter View Post
    start by simplifying the complex fraction ...

    \frac{\frac{1}{x+1} - \frac{1}{4}}{x-3} \cdot \frac{4(x+1)}{4(x+1)}
    Quote Originally Posted by SworD View Post
    Whenever you see a problem like this, try to simplify it to a rational function (quotient of two polynomials, such as \frac{4 - (x+1)}{4(x-3)(x+1)}, using various strategies like common denominators, etc. Then pull out any common factors. (You may need to find the roots.)
    Thank you all very much. I feel stupid now, but I think I got it. Could you tell me if this reasoning is correct?

    \frac{\frac{1}{x+1} - \frac{1}{4}}{x-3} \cdot \frac{4(x+1)}{4(x+1)} = \frac{4-(x+1)}{4(x-3)(x+1)} = \frac{-(x-3)}{4(x-3)(x+1)} = \frac{-1}{4x+4}
    Last edited by Diogenes; September 18th 2012 at 11:38 AM.
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    Re: Can't find this limit analytically

    Yes it is.
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