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Math Help - single algebraic fraction

  1. #1
    Junior Member
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    single algebraic fraction

    Write each expression as a single algebraic fraction.
    (1-xy^-1)^-1
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  2. #2
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    (1-(xy)^{-1})^{-1}

    Remember:
    a^{-1} = \frac{1}{a}

    So:
    (1-(xy)^{-1})^{-1} = \frac{1}{1-(xy)^{-1}} = \frac{1}{1-\frac{1}{xy}}

    Combine 1 and \frac{1}{xy}. Remember that 1 = \frac{xy}{xy}.

    \frac{1}{1-\frac{1}{xy}} = \frac{1}{\frac{xy}{xy}-\frac{1}{xy}} = \frac{1}{\frac{xy - 1}{xy}}

    Now, this expression can be rearranged like this:

    \frac{1}{\frac{xy - 1}{xy}} =  1 \cdot \frac{xy}{xy-1} = \frac{xy}{xy-1}
    Last edited by Chop Suey; August 11th 2008 at 01:30 PM.
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  3. #3
    Super Member wingless's Avatar
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    xy^{-1} can mean \frac{x}{y} too.
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  4. #4
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    If you meant xy^{-1} as Wingless pointed out:

    (1-xy^{-1})^{-1}

    = \frac{1}{1-\frac{x}{y}}

    = \frac{1}{\frac{y-x}{y}}

    = 1 \cdot \frac{y}{y-x} = \frac{y}{y-x}
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