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Simplifying a rational expression

  1. Aug 17, 2015 #1
    Given that we have the expression ##\displaystyle-\frac{1}{(x-2)(x-2)(x-3)}~\cdot~\sqrt{\frac{(x-2)^{2}}{(x-3)(x-1)}} ##, how do we simplify it, step by step? Specifically, I am concerned about the ##\sqrt{(x-2)^{2}}## term. Are we allowed to cancel this with the ##(x-2)## in the denominator?
  2. jcsd
  3. Aug 17, 2015 #2
  4. Aug 17, 2015 #3


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    I disagree. You have to be careful about signs. The square root of x squared is not always equal to x.

    Take, for instance, x=0 and evaluate the given expression before and after cancellation. Do the two give the same result?
  5. Aug 17, 2015 #4


    Staff: Mentor

    I agree with jbriggs444 here, and would add that ##\sqrt{x^2} = |x|##, which is something I mentioned in your other thread on rational expressions.
  6. Aug 18, 2015 #5


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    By the way- this is not a "rational function"!
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