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Math Help - Limits- Eliminating a zero denominator algebraically

  1. #1
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    Limits- Eliminating a zero denominator algebraically

    For:

    lim x-->1 x-1/((√x+3)-2)^2

    How would I go about eliminating this zero denominator?

    Thankyou
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  2. #2
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    Quote Originally Posted by katedew987 View Post
    For:

    lim x-->1 x-1/((√x+3)-2)^2

    How would I go about eliminating this zero denominator?

    Thankyou


    Multiply both numerator and denominator by the denominator's conjugate, \left(\sqrt{x+3}+2\right)^2 , and after some very little

    algebraic manipulation you'll get a very simple expression whose limit (which does NOT exist) is very easy to compute.

    Tonio

    Ps The above is true assuming you meant the expression \frac{x-1}{(\sqrt{x+3}-2)^2}
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