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Math Help - Simplify this equation

  1. #1
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    Simplify this expression

    Simplify: (a^{-1}+b^{-2})^{-1}

    I know that's simple. I can express that as:

    \frac{1}{\frac{1}{a}+\frac{1}{b^{2}}}

    The problem is that, to me, that doesn't look any simpler.

    I can't think of how else to express this. Is there another more appropriate answer?
    Last edited by jerry; August 21st 2008 at 05:14 AM.
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  2. #2
    Moo
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    Hi,
    Quote Originally Posted by jerry View Post
    Simplify: (a^{-1}+b^{-2})^{-1}

    I know that's simple. I can express that as:

    \frac{1}{\frac{1}{a}+\frac{1}{b^{2}}}

    The problem is that, to me, that doesn't look any simpler.

    I can't think of how else to express this. Is there another more appropriate answer?
    You can just transform 1/a + 1/bē into a single fraction (common denominator), it depends on what you mean by "simple"

    By the way, this is not an equation. An equation contains the = sign ! This is an expression ^^
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  3. #3
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    Hello, jerry!

    Simplify: . (a^{-1}+b^{-2})^{-1}

    I can express that as: . \frac{1}{\dfrac{1}{a}+\dfrac{1}{b^{2}}}

    The problem is that, to me, that doesn't look any simpler.

    You have a complex fraction . . . one with more than two "levels".
    . . We can and must simplify it further.


    Multiply top and bottom by the LCD, ab^2

    . . \frac{{\color{blue}ab^2}\cdot(1)}{{\color{blue}ab^  2}\cdot\left(\dfrac{1}{a}+\dfrac{1}{b^2}\right)} \;=\;\frac{ab^2}{b^2+a} \quad\hdots\quad see?

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  4. #4
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    OK. Thank you both for that!
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