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Factoring theory problem

  1. Sep 25, 2006 #1
    I know this must be a basic factoring question but I don't get it. Somewhere in the solution below there is an error which leads to an end result of 1 = 2. I'm supposed to find where the error lies.

    The factoring looks right. I think the error is in line three. you can only multiply or divide a factor (common factor between both sides) and can't subtract.... am I on the right track or just grasping at straws?

    Thanks for any help

    x = x
    x^2 = x^2
    x^2 − x^2 = x^2 − x^2
    x(x − x) = (x + x)(x − x)
    x = (x + x)
    x = 2x
    If we let x =1, then upon substitution we have
    (1) = 2(1)
    1 = 2
  2. jcsd
  3. Sep 25, 2006 #2
    ab=ac implies b=c only if a does not equal 0. So you can't get from x(x-x) = (x+x)(x-x) to x = (x+x) since (x-x)=0. You're effectively "dividing by zero" in that step. This is one of the many reasons division by zero isn't allowed.
  4. Sep 25, 2006 #3


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    Line 3 is fine.

    Maybe try substituting x=1 in each line. You should be able to spot which line contains the first error, then look at the last operation you did carefully.
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