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Math Help - simplify

  1. #1
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    simplify

    x/(x-2) - (x-6)/(x-4)
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  2. #2
    Junior Member mathmonster's Avatar
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    if u have

    x/(x-2) - (x-6)/(x-4) = 0

    then multiply by x-4 and x-2 to get

    x(x-4) - (x-6)(x-2)

    the multiply out the brackets

    x^2 - 4x - x^2 + 8x - 12 = 0

    then collect like terms to get

    4x - 12 = 0,

    so x = 3
    Last edited by mathmonster; November 14th 2007 at 05:18 PM. Reason: wrong answer
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  3. #3
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    its not equal to zero though. we dont have to solve, so we cant multiply my (x-2)(x-4) because that would change the function

    4x-12 does not equal the original
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  4. #4
    Junior Member mathmonster's Avatar
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    oh right, sorry i mistook the question, ill come back with the answer hopefully
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  5. #5
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    any other ideas
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  6. #6
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    x/(x-2) - (x-6)/(x-4)

    GCM- greatest common denominator
    Or is it LCD - least common denominator? I think GCM.

    either way, get a common, meaning equal, denominator (bottom part of each fraction) for both fractions.

    So,

    \frac {x*(x-4)}{(x-2)*(x-4)}-\frac {(x-6)*(x-2)}{(x-4)*(x-2)}


    Make it all one fraction, now that we have a common denominator.

    Subtract the numerator, the tops, if possible to get rid of terms.
    ex. (x-2)- (x-2) and cancel (not saying exists above, its just an example)

    There you go.
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  7. #7
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    It's LCD. Lowest Common Denominator. But "lowest" isn't all that important here because all you do is multiply that two denominators together.

    So from the post above:

    The (x-4) and (x-2) cancel out leaving you with:

    x-x-6 / x-2-x-4

    which simplifies to:

    -6/-6 which is 1.

    I hope I'm right. I would double check. :P
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