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Rationalizing the numerator with limits

  1. May 21, 2012 #1
    1. The problem statement, all variables and given/known data

    Screenshot2012-05-22at123618AM.png



    3. The attempt at a solution

    I don't see how the above step is legal. I plugged in 4 for z and 9 for z and it works, but what is this move called? it's neither rationalizing the numerator nor rationalizing the denominator.
     
  2. jcsd
  3. May 22, 2012 #2

    Dick

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    It's called factoring. z-x=(sqrt(z)-sqrt(x))*(sqrt(z)+sqrt(x)). It should work ok as long as z and x are nonnegative. I think you can assume that because otherwise your numerator isn't very well defined.
     
  4. May 22, 2012 #3
    FOIL the denominator in the second step and you'll get back what you started with.
     
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