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Math Help - Expression

  1. #1
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    Expression

    Simplify the expression:

    \frac{1}{1-x}-\frac{1}{1+x}-\frac{1}{1+x^2}-\frac{1}{1+x^4}-\frac{1}{1+x^8}
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  2. #2
    MHF Contributor
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    Talking

    Quote Originally Posted by Apprentice123 View Post
    Simplify the expression:

    \frac{1}{1-x}-\frac{1}{1+x}-\frac{1}{1+x^2}-\frac{1}{1+x^4}-\frac{1}{1+x^8}
    Convert the fractions to their common denominator (surprising simple), and then combine the numerators (nasty!).

    \frac{(1+x)(1+x^2)(1+x^4)(1+x^8)}{1-x^{16}}-\frac{(1-x)(1+x^2)(1+x^4)(1+x^8)}{1-x^{16}}

    . . . -\frac{(1-x^2)(1+x^4)(1+x^8)}{1-x^{16}}-\frac{(1-x^4)(1+x^8)}{1-x^{16}}-\frac{(1-x^8)}{1-x^{16}}

    ...I think that's right....
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  3. #3
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    Now, multiply each numerator and then combine all the like terms ...
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