Results 1 to 3 of 3
Like Tree2Thanks
  • 1 Post By HallsofIvy
  • 1 Post By Prove It

Thread: Adding Rational Expressions

  1. #1
    Newbie
    Joined
    Nov 2012
    From
    United States
    Posts
    18

    Adding Rational Expressions

    Problem: $\displaystyle \frac{x - 8}{x^2 - 4} + \frac{3}{x^2-2x}$

    Answer: $\displaystyle \frac{x-3}{x(x+2)}, x\not=2 $

    What I ended up with: $\displaystyle \frac{x^2-5x+6}{x(x^2 - 4)} $

    Any help on how to do problems like this would be great as well. I feel like I was doing everything correctly, but now that I'm at the end I don't see any way to make my answer look like the one in the book.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Apr 2005
    Posts
    19,724
    Thanks
    3008

    Re: Adding Rational Expressions

    Very close. All you need to do is observe that $\displaystyle x^2- 5x+ 6= (x- 2)(x- 3)$.

    Even if you are not good at factoring in general, you should recognize that $\displaystyle x^2- 4= (x- 2)(x+ 2)$, which you apparently did to get the "least common denominator" and then check for common factors in the numerator and denominator. And you can do that by evaluating $\displaystyle 0^2- 5(0)+ 6= 6$ so x- 0= x is not a factor. $\displaystyle (-2)^2- 5(-2)+ 3= 17$ so x+ 2 is not a factor. But $\displaystyle 2^2- 5(2)+6= 0$ so x- 2 is a factor of $\displaystyle x^2- 5x+ 6$.
    Thanks from fogownz
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor
    Prove It's Avatar
    Joined
    Aug 2008
    Posts
    12,880
    Thanks
    1946

    Re: Adding Rational Expressions

    Quote Originally Posted by fogownz View Post
    Problem: $\displaystyle \frac{x - 8}{x^2 - 4} + \frac{3}{x^2-2x}$

    Answer: $\displaystyle \frac{x-3}{x(x+2)}, x\not=2 $

    What I ended up with: $\displaystyle \frac{x^2-5x+6}{x(x^2 - 4)} $

    Any help on how to do problems like this would be great as well. I feel like I was doing everything correctly, but now that I'm at the end I don't see any way to make my answer look like the one in the book.
    Notice that $\displaystyle \displaystyle \begin{align*} x^2 - 4 = (x - 2)(x + 2) \end{align*}$ and $\displaystyle \displaystyle \begin{align*} x^2 - 2x = x(x - 2) \end{align*}$. So the lowest common denominator is $\displaystyle \displaystyle \begin{align*} x(x-2)(x+2) \end{align*}$. You should get into the habit of keeping things factorised until the end, as it makes cancelling a lot easier.
    Thanks from fogownz
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Adding Rational Expressions
    Posted in the Algebra Forum
    Replies: 4
    Last Post: Aug 12th 2010, 08:02 AM
  2. Adding Rational Expressions
    Posted in the Algebra Forum
    Replies: 5
    Last Post: Jul 26th 2010, 03:52 PM
  3. Adding rational expressions
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: Feb 22nd 2010, 01:10 PM
  4. adding rational expressions
    Posted in the Algebra Forum
    Replies: 1
    Last Post: Jul 27th 2008, 12:05 PM
  5. Adding rational expressions
    Posted in the Math Topics Forum
    Replies: 2
    Last Post: Jul 5th 2008, 09:25 PM

Search Tags


/mathhelpforum @mathhelpforum