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Homework Help: 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.
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