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Math Help - Find the range of values of x

  1. #1
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    Find the range of values of x

    Find the range of values of x for which |\frac{2x+5}{x^2-4}|\geqslant \frac{1}{5}
    Last edited by Punch; May 7th 2011 at 10:51 PM.
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    Quote Originally Posted by Punch View Post
    Find the range of values of x for which |\frac{2x+5}{x^2-4}|≥\frac{1}{5}
    Show us what you know. Hint: Can you find any horizontal asymptotes? Vertical asymptotes?

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  3. #3
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    So you want to find x so that \frac{2x+ 5}{x^2- 4}\ge \frac{1}{5} or \frac{2x+ 5}{x^2- 4}\le -\frac{1}{5}

    If |x|> 2, then x^2- 4> 0 so those are the same as
    5(2x+ 5)= 10x+ 25> x^2- 4 and
    5(2x+ 5)= 10x+ 25> 4- x^2
    which are, of course, the same as
    x^2- 10x- 29> 0 and
    x^2+ 10x+ 21> 0
    What values of x> 2 or x< -2 satisfy those?

    If |x|< 2 then x^2- 4< 0 so those are the same as
    5(2x+ 5)= 10x+ 25< x^2- 4 and
    5(2x+ 5)= 10x+ 25< 4- x^2 which are the same as
    x^2- 10x- 29< 0 and
    x^2+ 10x+ 21< 0
    What values of x, -2< x< 2, satisfy those?
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  4. #4
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    Multiply out and get it all on one side, you will have a quadratic.
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