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Math Help - complex fractions

  1. #1
    Newbie 21_knip's Avatar
    Joined
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    complex fractions

    what is the technique when solving complex fractions?

    a
    --------
    1 - 1
    ----
    1+ 1
    ---
    a-1
    Attached Files Attached Files
    Last edited by 21_knip; January 13th 2009 at 09:11 PM. Reason: just try to see the attachment. i ifnd it hard to input it here.
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  2. #2
    MHF Contributor chiph588@'s Avatar
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    Champaign, Illinois
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    invert and multiply
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  3. #3
    MHF Contributor
    Grandad's Avatar
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    South Coast of England
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    1

    Fractions

    Hello 21_knip
    Quote Originally Posted by 21_knip View Post
    what is the technique when solving complex fractions?

    a
    --------
    1 - 1
    ----
    1+ 1
    ---
    a-1
    If I read your attachment correctly, start with the 1 and the fraction at the bottom first, and write them over a common denominator; like this:

    1 + \frac{1}{a-1} = \frac{a-1}{a-1}+\frac{1}{a-1}

    = \frac{a-1+1}{a-1}

    = \frac{a}{a-1}

    You now need 1 over this answer; that's \frac{1}{\frac{a}{a-1}}

    This is simply the reciprocal of the fraction: turn it 'upside-down': \frac{a-1}{a}

    Now you do a similar thing for the remaining 1 and this new fraction:

    1 - \frac{a-1}{a} = \frac{a}{a} - \frac{a-1}{a}

    = \frac{a-a{\color{red}+}1}{a} Watch that sign!

    = \frac{1}{a}

    And so finally (as chiph588@ said) invert and mulitply:

    \frac{a}{\frac{1}{a}}

    = a \times \frac{a}{1}

    = a^2

    I hope you followed all that.

    Grandad
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