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I think this is simple but I just cant work out how!

  1. Apr 28, 2010 #1
    how does [tex]\frac{1/a -1/b}{1/a+1/b}= \frac{b-a}{b+a}[/tex]

    Ive been trying to work this out for ages

    thanks
     
  2. jcsd
  3. Apr 28, 2010 #2
    It's simple algebra. Here's a few hints.

    The right hand side, as given, is this:

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

    But this can be written more clearly as:

    [tex](\frac{1}{a} - \frac{1}{b})(\frac{1}{a} + \frac{1}{b})^{-1}[/tex]

    From there, apply algebraic operations to this expression until it equals the right hand side.
     
  4. Apr 28, 2010 #3
    Think about what value you need to multiply the left hand side with to make it equal the right hand side.
     
  5. Apr 28, 2010 #4
    Multiply by ab in both the numerator and the denominator. This is multiplying by one.
     
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