1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Solving Rational Equation

  1. Apr 25, 2010 #1
    1. The problem statement, all variables and given/known data

    Solve for x.

    2. Relevant equations

    3/2 + 2/2x-4 = 1/x-2

    3. The attempt at a solution

    LCD = 2(x-2)

    3/2 + 2/2x-4 = 1/x-2 Mult. all terms by 2(x-2)

    3x - 6 + 2 = 2

    3x = 6

    x = 2

    What am I missing here?
     
  2. jcsd
  3. Apr 25, 2010 #2
    Why would you think you're missing something?
     
  4. Apr 25, 2010 #3
    No idea, really. I think I followed all the correct steps. I also re-checked my class notes and this happens to be one of the exercises done in class by my professor. However, he solved the equation in a different and longer manner but with the same result (even though there is a (x-2)(x-2) = x^2 - 4 ?).

    It's probably the inconsistent solution I obtain that bothers me.
     
  5. Apr 25, 2010 #4
    Well, x = 2 makes your denominators zero, so that can't be the right answer.

    Suppose you reduce the second term of the equation by canceling the 2.

    Now you have 3/2 + 1/(x-2) = 1/(x-2).

    That equation doesn't make any sense, right? Subtracting 1/(x-2) from both sides gets you 3/2 = 0.

    There aren't any solutions to this equation.
     
  6. Apr 25, 2010 #5
    Well, that confirms my suspicion. This is the first exercise in this assignment that has no solutions.

    Thank you for your time and assistance!
     
  7. Apr 26, 2010 #6
    Yeah, you really weren't missing anything per se, you just didn't make the conclusion that x = 2 isn't in the domain of the function, as hgfalling illustrated.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Solving Rational Equation
Loading...