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Small part of a larger problem

  1. Sep 12, 2009 #1
    1. The problem statement, all variables and given/known data
    I am trying to figure out of [tex]\frac{9}{x+h}[/tex] can be split into some thing like
    [tex]\frac{9}{x} + ?[/tex]

    2. Relevant equations

    3. The attempt at a solution
    I am not sure what to do. I am trying to do this as part of a larger limits problem.
    Last edited: Sep 12, 2009
  2. jcsd
  3. Sep 12, 2009 #2
    I don't believe you can change one to the other. The difference between 9/(x + h) and 9/x is that the first is shifted -h units to the left of the graph of 9/x. 9/x + something would shift the graph of 9/x up something units.
  4. Sep 12, 2009 #3
    You would need to add it to a fraction whose denominator 'a' had the property xa = x + h, or a = (x + h)/x. Unfortunately, there is no fraction that you can add that will not affect the numerator as well.
  5. Sep 13, 2009 #4
    Damn, ok thanks for your help, both of you.
  6. Sep 14, 2009 #5


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    What you can do is get a common denominator and subtract fractions.
    [tex]\frac{9}{x+h}- \frac{9}{x}= \frac{9x}{x(x+h)}- \frac{9(x+h)}{x(x+h)}[/tex]
    [tex]= \frac{9x- 9(x+h)}{x(x+h)}= \frac{-9h}{x(x+h)}[/tex]
    and you should be able to complete the derivative.
    Last edited: Sep 14, 2009
  7. Sep 14, 2009 #6
    :surprisedAhhhhh, I see said the blind man to the deaf dog with no ears. Thank you!!!!!

    Btw how did you figure out that thats what I was trying to do? That was pretty amazing. :D
    Last edited: Sep 14, 2009
  8. Sep 14, 2009 #7


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    Hey, after some time here you get used to figuring out what people are really asking!
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