Results 1 to 4 of 4

Math Help - Limit of a rational with polynomials

  1. #1
    Member nautica17's Avatar
    Joined
    Aug 2009
    Posts
    121

    Limit of a rational with polynomials

    I'm stuck on this practice problem.. and it's the algebra that is getting to me. Take a look:

    lim x-> 2 of ( (x^3 + 3x^2 - 12x + 4) / (x^3 - 4x) )

    I've figured that I factor out the top and bottom and I've done so with the denominator and got x(x-2)(x+2), but the numerator is what I am stuck on. Can anyone push me in the right direction? I'm getting this as my numerator: (x^2 - 4)(x+3)(3x+1) ... and that obviously makes no sense what so ever.

    Any help please?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,605
    Thanks
    1574
    Awards
    1
    Quote Originally Posted by nautica17 View Post
    lim x-> 2 of ( (x^3 + 3x^2 - 12x + 4) / (x^3 - 4x) )
    x^3+3x^2-12x+4=(x-2)(x^2+5x-2)
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member nautica17's Avatar
    Joined
    Aug 2009
    Posts
    121
    Quote Originally Posted by Plato View Post
    x^3+3x^2-12x+4=(x-2)(x^2+5x-2)
    Hmm.. well that works. Thank-you. If it's not too much trouble could you show me how to do that? I cannot figure out how to pull the (x-2) out.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,605
    Thanks
    1574
    Awards
    1
    Quote Originally Posted by nautica17 View Post
    Hmm.. well that works. Thank-you. If it's not too much trouble could you show me how to do that? I cannot figure out how to pull the (x-2) out.
    Because x=2 is a root of the numerator then (x-2) must be a factor.
    So use simple long division.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 1
    Last Post: April 20th 2011, 10:49 AM
  2. Polynomials and rational functions
    Posted in the Pre-Calculus Forum
    Replies: 5
    Last Post: July 12th 2010, 03:50 AM
  3. product of rational polynomials
    Posted in the Pre-Calculus Forum
    Replies: 1
    Last Post: April 6th 2009, 09:50 AM
  4. Rational Root Theorem for polynomials...
    Posted in the Algebra Forum
    Replies: 2
    Last Post: April 22nd 2008, 02:20 PM
  5. Replies: 0
    Last Post: November 29th 2007, 11:12 AM

Search Tags


/mathhelpforum @mathhelpforum