Results 1 to 3 of 3
Like Tree1Thanks
  • 1 Post By emakarov

Math Help - Simplifying polynomial fractions - Equality question

  1. #1
    Newbie
    Joined
    Jul 2012
    From
    California
    Posts
    1

    Simplifying polynomial fractions - Equality question

    I am studying the simplification of polynomial fractions. My textbook has the example of:

    \dfrac{2x+6}{x^2-9} = \dfrac{2}{x-3} : factored out (x+3) from the numerator and denominator

    My confusion is over the sense of 'equality' of the 2 expressions. I expected to be able to use either expression interchangeably as the definition for a function. However,

    \ f(x) = \dfrac{2x+6}{x^2-9} is undefined for x = { 3, -3 }

    \ f(x) = \dfrac{2}{x-3} is undefined for x = { 3 }

    The domains of the functions differ. It appears that 'information' was lost in the simplification of the original expression.

    Are the 2 expressions not really "equal"? Am I misunderstanding something about the concept of equality with regard to expressions?
    Last edited by ForumUser2; July 24th 2012 at 03:53 PM.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Joined
    Oct 2009
    Posts
    5,527
    Thanks
    773

    Re: Simplifying polynomial fractions - Equality question

    Quote Originally Posted by ForumUser2 View Post
    Are the 2 expressions not really "equal"?
    That's right. As numbers, \dfrac{2x+6}{x^2-9} and \dfrac{2}{x-3} are equal iff x\ne-3. To compare these expressions as functions, we must equip each of them with a domain. As long as those domains do not include -3, they are equal as functions (in the set-theoretic sense). With their natural, i.e., maximal, domains, they are different as functions because their domains are different.

    In the process of transformations (e.g., when solving an equation), it is important to check if each equality is a true identity, i.e., holds for all values of variables. Similarly, it is important to check if two equalities or inequalities are truly equivalent, i.e., are both true or both false for all values of variables.
    Thanks from ForumUser2
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Jul 2012
    From
    Pakistan
    Posts
    4

    Re: Simplifying polynomial fractions - Equality question

    I just love your blog.Thanks for posting it.i have something that someone comeback again….there is a lot of useful information a person can get from here…Web DevelopmentI must say,well done...i visited it daily,what a colourful blog it is....colours attracted me a lot...Free Legal Advice.i visited it daily,what a colourful blog it is.... a very decent and nice blog...i like it so very much...
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Simplifying fractions.
    Posted in the Algebra Forum
    Replies: 5
    Last Post: May 1st 2011, 05:21 PM
  2. equality problem with fractions
    Posted in the Algebra Forum
    Replies: 4
    Last Post: April 20th 2010, 04:54 AM
  3. Quick Polynomial simplifying question
    Posted in the Pre-Calculus Forum
    Replies: 4
    Last Post: February 14th 2009, 06:52 AM
  4. Simplifying Fractions
    Posted in the Algebra Forum
    Replies: 3
    Last Post: May 20th 2008, 07:05 AM
  5. Simplifying Fractions - Am I right?
    Posted in the Algebra Forum
    Replies: 13
    Last Post: August 28th 2006, 06:49 PM

Search Tags


/mathhelpforum @mathhelpforum