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Don't understand how to simplify this limit

  1. Nov 29, 2009 #1
    1. The problem statement, all variables and given/known data

    lim
    x->-1 x^1/3 + 1 / x + 1 = x^1/3 + 1 / x + 1 ((x^2/3 - x^1/3 + 1) / (x^2/3 - x^1/3 + 1))

    = x + 1 / (x + 1)(x^2/3 - x^1/3 + 1)

    cancel out and done


    I don't understand how to know what reciprocal to multiply in cases like these to make it work.
    Please help.
     
  2. jcsd
  3. Nov 29, 2009 #2

    Dick

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    Science Advisor
    Homework Helper

    Your formatting is horrible. Use more parentheses, ok? I think you mean limit x->(-1) of (x^(1/3)+1)/(x+1). It might be a little clearer if you change variables first and let u=x^(1/3). So u->(-1) also and now your expression is (u+1)/(u^3+1). Can you factor (u^3+1)=(u+1)*(something)? Use polynomial division to divide u^3+1 by u+1 if you don't know the answer.
     
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