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Pulling out -1 from denominator?

  1. Nov 16, 2007 #1
    I know this might seem trivial but I've never had a teacher cover this even though I've had the whole "factor out -1 from numerator " class.

    I was thinking of the cases but I haven't found a contradiction to:

    [tex]\frac{a}{b-c}=-1\frac{a}{c-b}[/tex]

    so is this always true?
     
  2. jcsd
  3. Nov 16, 2007 #2
    Obviously. After all (-x)/y=x/(-y)=-(x/y).
     
  4. Nov 16, 2007 #3

    CRGreathouse

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    It's true. It's a special case of

    [tex]\frac{1}{ab}=\frac1a\cdot\frac1b[/tex]
     
  5. Nov 16, 2007 #4
    thanks
    I've always wondered about that...
    for some reason no teacher I've had has ever done that manipulation.
     
  6. Nov 17, 2007 #5

    arildno

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    You might try to prove the following statements:
    [tex]\frac{1}{1}=1, \frac{1}{(-1)}=(-1)*\frac{1}{1}=(-1)[/tex]
     
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