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Simplify factors

  1. Nov 2, 2004 #1
    Hi! I'm new to those forums, so I just want to say "Hello everbody!". To my question: How can I simplify [tex]\frac{\frac{1}{x+\Delta x}-\frac{1}{x}+ \frac{1}{x^2}\Delta x}{\Delta x}[/tex] I've spent some hours on google, but no result. Just tell me the name of the method and I'm really gratefull!
     
  2. jcsd
  3. Nov 2, 2004 #2
    First simplify [itex]\frac{1}{x+\Delta x}-\frac{1}{x}+ \frac{1}{x^2}\Delta x}[/itex] by finding a common denominator.
     
  4. Nov 2, 2004 #3
    Hmm... Now I've [tex]\frac{x^2\Delta x}{x^3+x^2\Delta x}[/tex] for the nominator. Is that an inprovment?
     
    Last edited: Nov 2, 2004
  5. Nov 2, 2004 #4
    Well, yes, but I'm afraid it's wrong. This is very sloppily written (I've left out some parantheses), and h = delta x:

    1/(x+h) - 1/x + h/x^2 =
    x^2/x^2(x+h) - x(x + h)/x^2(x + h) + h(x + h)/(x + h)x^2 =
    ( x^2 - x(x + h) + h(x + h) ) / ((x + h)x^2) =
    ( x^2 - x^2 - xh + hx + h^2 ) / ((x + h)x^2) =
    h^2 / ((x + h)x^2).

    Upon division by h, we get

    (1/(x+h) - 1/x + h/x^2) / h = h / ((x + h)x^2).
     
  6. Nov 2, 2004 #5
    Ah, nice. I think I got it now. Thanks!
     
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