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Problem composing a rational function with itself.

  1. Jan 29, 2009 #1
    I'm trying to compose [tex]f(x)= x + \frac{1}{x}[/tex] with itself. e.g. [tex]f \circle f[/tex]

    I have [tex] x + \frac{1}{x} + \frac{1}{x+(1/x)} [/tex]

    Now I multiplied [tex] \frac{1}{x + (1/x)} * \frac{x}{x} [/tex] and I got:

    [tex] x + \frac{1}{x} + \frac{x}{x^2+1} [/tex]

    This is not the correct answer according to the book.
    Books is:

    [tex] \frac{x^4+3x^2+1}{x(x^2+1)} [/tex]

    I have no idea how they got that. I can't get a common denominator and get that.
     
    Last edited: Jan 29, 2009
  2. jcsd
  3. Jan 29, 2009 #2

    Dick

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    Try a forward slash on the final [tex]. But your answer is also correct. Put everything over a common denominator of x*(x^2+1).
     
  4. Jan 29, 2009 #3
    Thank you very very very much. My first 100 in calc so far awaits me tomorrow!
     
  5. Jan 29, 2009 #4

    Dick

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    Good luck!
     
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