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Stuck on the first chapter of Apostol:

  1. Oct 28, 2006 #1
    I've been going over the book and everything was going well until I got to this question:

    [tex]\frac{1} {2 + \sqrt{4 - x^2}} = \frac{2 - \sqrt{4 - x^2}} {x^2}[/tex]

    Tried with partial fractions but that does not work. I also tried to split the fraction but I don't know how to get the x^2 at the bottom. In short I'm completely lost and that looks like black magic to me. I'd appreciate it if anyone has a link to explain what's going on here.

    Edit: Messed up the latex. If you click on it the correct code shows up. Not sure how I can refresh the originally posted one.
     
    Last edited: Oct 28, 2006
  2. jcsd
  3. Oct 28, 2006 #2
    He just rationalized the denominator.

    [tex]\frac{1} {2 + \sqrt{4 - x^2}} \ \frac{2-\sqrt{4 - x^2}}{2-\sqrt{4 - x^2}} = \frac{2 - \sqrt{4 - x^2}} {x^2} [/tex]

    Note the denominator is a difference of squares: [tex] a^{2}-b^{2} [/tex]
     
    Last edited: Oct 28, 2006
  4. Oct 28, 2006 #3
    Thanks a lot, I was stuck on that for a long time.
     
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