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Simplifying rational functions with common factors

  1. Jul 24, 2009 #1
    1. The problem statement, all variables and given/known data

    Simply these rational functions: [[tex]\sqrt{(X^2)+12}[/tex]-4]/(X-2)

    (2-[tex]\sqrt{(X^2)-5}[/tex])/(X+3)

    (X-1)/([tex]\sqrt{X+3}[/tex]-2)

    2. Relevant equations

    The only example in the book used the technique of multiplying the numerator and denominator by the function p(x) if p(x) is the function in the above equations with a square root in it, except they switched the sign.

    3. The attempt at a solution

    For example, for the equation [[tex]\sqrt{(X^2)+12}[/tex]-4]/(X-2) you would multiply both sides by [[tex]\sqrt{(X^2)+12}[/tex]+4], but this yields ([(x^2)+12]-16)/(X-2)([tex]\sqrt{(X^2)-12}[/tex]+4), which I'm not sure simplifies. Could you please explain how to solve these problems? Thank you.
     
  2. jcsd
  3. Jul 25, 2009 #2
    Nevermind, I figured out all the answers!
     
  4. Jul 25, 2009 #3

    HallsofIvy

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    Did you figure out that those aren't rational functions?
     
  5. Jul 25, 2009 #4
    Indeed I did.
     
  6. Jul 25, 2009 #5

    HallsofIvy

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    Excellent!
     
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