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Can't simplify this fraction

  1. Oct 6, 2008 #1
    Fraction is:

    [tex]\frac{1-e^{-x}}{1-e^{x}}[/tex]

    and it's meant to go to:

    [tex]-e^{-x}[/tex]

    I can't make it look like it needs to. I tried splitting it up but that goes nowhere.

    What other strategies are there for simplifying fractions like this?

    Thanks for any help.
     
  2. jcsd
  3. Oct 6, 2008 #2

    Borek

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    Staff: Mentor

    [tex]1-e^{-x} = -e^{-x}(...)[/tex]
     
  4. Oct 6, 2008 #3
    [tex] 1 - e^{-x} = -e^{-x} + 1 [/tex]

    ? Still don't get it sorry...
     
  5. Oct 6, 2008 #4

    Borek

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    Staff: Mentor

    [tex]
    1-e^{-x} = -e^{-x}(... - 1)
    [/tex]
     
  6. Oct 6, 2008 #5

    gabbagabbahey

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    Homework Helper
    Gold Member

    What do you get when you multiply both the numerator and the denominator by [itex]-e^{-x}[/itex]?
     
  7. Oct 6, 2008 #6

    HallsofIvy

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    Staff Emeritus
    Science Advisor

    Or multiply numerator and denominator by the "conjugate", 1+ e-x.
     
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