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Finding Limits

  1. Jan 18, 2014 #1
    1. The problem statement, all variables and given/known data
    Find the following limit

    lim (1/(x-1))-(2/(x^2-1))

    2. Relevant equations

    3. The attempt at a solution
    I tried simplifying the equation into one fraction by finding a common denominator. I did this to try to get a denominator where I could plug 1 in without it equaling 0. It didn't work, i ended up with (x^2-2x)/(x^3-x^2-x+1). I feel like I went in the wrong direction from the beginning. If someone could tell me what detail I'm missing it would be greatly appreciated! Thanks!
  2. jcsd
  3. Jan 18, 2014 #2


    Staff: Mentor

    The LCD is x2 -1, not (x - 1) (x2 - 1). All you need to do is multiply the first fraction by x + 1 over itself.
  4. Jan 18, 2014 #3
    I did that which left me with (x - 1)/(x^2 - 1) but that still makes the expression undefined when I input 1. I know the answer is 1/2, but I still don't see it. Does the expression mean 1/2 and I'm missing it or is there more computation involved?
  5. Jan 18, 2014 #4


    Staff: Mentor

    There's a little bit more to do. Factor the denominator and cancel the common factors in top and bottom.
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