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Reaching my limits

  1. Feb 5, 2013 #1
    1. The problem statement, all variables and given/known data
    lim x->4 (1/((sqrt x)-2))-4/(x-4)

    2. Relevant equations

    3. The attempt at a solution I have made several stabs at this problem. First I tried using values very close to 4 (e.g. sqrt of 4.001) Then I tried rationalizing the expression 1/((sqrt x) -2). That did not work. I also tried the LCD b. Nothing gets me closer to the answer which is 1/4. Pleae help.
  2. jcsd
  3. Feb 5, 2013 #2
    Add up the two fractions.
  4. Feb 5, 2013 #3
    like so: x-4sqrtx+4/(sqrtx-2)(x-4) Then what?
  5. Feb 5, 2013 #4
  6. Feb 5, 2013 #5


    Staff: Mentor

    I would appreciate it, as well. Here's what you wrote:

    $$ x - 4\sqrt{x} + \frac{4}{\sqrt{x} - 2} (x - 4)$$

    This is probably not what you meant, though.
  7. Feb 8, 2013 #6
    [itex] lim x-> 4 (1/sqrt (x) -2)-(4/x-4)[/itex]

    Here is the LaTex version of the problem Thanks for your help leading me to LaTex. I am still unable to solve the problem. When I combine the fractions using a common denominator I get:
    [itex] (x-4)(sqrt (x) -2)/(Sqrt (x)+2)(x-2)[/itex]
  8. Feb 8, 2013 #7


    Staff: Mentor

    I don't see how you got that.
    Starting from here:
    $$ \frac{1}{\sqrt{x} - 2} - \frac{4}{x - 4}$$

    the denominator will be (√x - 2)(x - 4), and not (√x + 2)(x - 2) as you show.

    It wouldn't hurt to review some basic algebra, especially how to add fractions.
    Last edited: Feb 8, 2013
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