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Thread: Simplifying Complex Algebraic Fractions

  1. #1
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    Simplifying Complex Algebraic Fractions

    Need Help figuring out the following:

    Simplying Complex Algebraic Fractions:

    $\displaystyle \displaystyle \frac {y - \frac {x^2+y^2}{y}} {\frac {1}{x} - \frac {1}{y}}$

    The book equates this to this:

    $\displaystyle \displaystyle \frac {\frac {y^2 - (x^2+y^2)}{y}}{\frac {y-x}{xy}} $

    It says in the book that this step reduces the numerator and denominator to single fractions. That's fine but doesn't say how it's done. I can see the top fraction you can get by:

    $\displaystyle \displaystyle \frac {(y)(y)+(x^2+y^2)}{y}$

    But i'm still unsure of that and don't know about the bottom fraction. I would normally look to multiply like

    $\displaystyle \displaystyle \frac {(xy)(1)}{x} - \frac {(xy)(1)}{y}$

    then cancel out the x and y's leaving:

    $\displaystyle y-x$

    Any suggestions advice would be great.

    Cheers

    BIOS
    Last edited by BIOS; Sep 25th 2010 at 10:30 AM.
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  2. #2
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    1/x - 1/y is simplified to y/xy - x/xy and u put them together into (y-x)/xy.
    and the top fraction u just y^2/y to get a common denominator.
    cause if u have 1/2 + 1/4 then u simplify it to 2/4 + 1/4 which u further simplify into (2 + 1) / 4
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  3. #3
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    Quote Originally Posted by BIOS View Post
    Need Help figuring out the following:

    Simplying Complex Algebraic Fractions:

    $\displaystyle \displaystyle \frac {y - \frac {x^2+y^2}{y}} {\frac {1}{x} - \frac {1}{y}}$
    Multiply both numerator and denominator by $\displaystyle xy$.

    We get $\displaystyle \displaystyle \frac {xy^2 - x^3-xy^2} {y-x}=\frac{-x^3}{y-x}$
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  4. #4
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    Hey guys thanks for the replies.

    Quote Originally Posted by Plato View Post
    Multiply both numerator and denominator by $\displaystyle xy$.

    We get $\displaystyle \displaystyle \frac {xy^2 - x^3-xy^2} {y-x}=\frac{-x^3}{y-x}$
    Hey plato. That's the answer alright. Still don't understand the books method/step in the example i posted above!

    Neither do i see how you can get to xy as a common factor so easily!

    Care to explain your method a little more? Would be most appreciated
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  5. #5
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    Within the complex fraction there are three 'smaller' fractions.
    The common denominator of all three is $\displaystyle xy$
    That is all there is to it.
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  6. #6
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    Yeah that makes perfect sense mate thanks. Think i need to do a quick revision on fractions!

    Cheers

    B
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