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Problem stating: if A = x - 1/x, find A - 1/A

  1. Jun 23, 2004 #1
    I have a math problem stating:
    if A = x - 1/x, find A - 1/A

    I have no clue as to how to solve this. Any insight would be greatly appreciated.
  2. jcsd
  3. Jun 23, 2004 #2
    You have that:

    A = x - 1/x
    1/A = 1/(x - 1/x)

    Then A - 1/A = what?
  4. Jun 23, 2004 #3
    Im sure this is easy but Im completely missing the logic. I havent done this kind of math in a while and hoping you could explain the logic.
  5. Jun 23, 2004 #4


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    Just simplify the fractions...

    [tex] A = x - \frac {1}{x} = \frac{x^2 - 1}{x} [/tex]

    [tex]So, ~ 1/A = \frac {x} {x^2 -1}[/tex]

    [tex] So, ~A - 1/A = \frac{x^2 - 1}{x} - \frac {x} {x^2 -1}[/tex]

    Take the lcm and simplify.
  6. Jun 23, 2004 #5
    Thanks Gokul43201:

    Ok, now I got it.
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