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Homework Help: Rationalizing a numerator

  1. Sep 11, 2011 #1
    1.
    Haven't done this type of math in a long time, here's the question:
    1. Rationalize the numerator
    a) (√x - 3) / (x - 9)


    Can't get the answer for the life of me. The textbook says (1)/(√x - 3)

    the / dictates division.




    2. Relevant equations
    Question: (√x - 3) / (x - 9)
    Answer: (1)/(√x - 3)




    3. The attempt at a solution

    I multiplied the top and bottom by the conjugate of the numerator (√x + 3)
    and ended up getting (x-9)/(x√x + 3x - 9√x - 27)

    and I get stumped here.
     
  2. jcsd
  3. Sep 11, 2011 #2

    LCKurtz

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    Instead of multiplying the denominator out like that, leave it factored and see if you can cancel factors.
     
  4. Sep 11, 2011 #3

    symbolipoint

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    From here, which looks good, (x-9)/(x√x + 3x - 9√x - 27)
    = [itex]\frac{x-9}{\sqrt{x}(x-9)+3(x-9}[/itex]
    = [itex]\frac{x-9}{(x-9)(\sqrt{x}-3)}[/itex]
    ... can then be simplified.
     
  5. Sep 11, 2011 #4
    Alright, I got it guys!
    Thanks :)
     
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