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Thread: Trouble with Rational Expression Division

  1. #1
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    Trouble with Rational Expression Division

    Hello, everybody. I attempted to solve a rational expression which requires division and apparently got the wrong answer. Here's the expression:

    $\displaystyle

    \frac {\frac {x^2 - y^2}{xy}}{\frac {x - y}{y}}

    $

    The steps I followed are as such:

    1. (Turn it into multiplication):

    $\displaystyle

    \frac {x^2 - y^2}{xy} * \frac {y}{x - y}

    $

    $\displaystyle

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

    $

    2. Multiply:

    $\displaystyle

    \frac {yx^2 - y^3}{yx^2 - xy^2}

    $

    3. Simplify:

    $\displaystyle

    \frac {y}{x}

    $

    However, I checked the answer and apparently it's:

    $\displaystyle

    \frac {x + y}{x}

    $

    I'm not sure what exactly I did wrong in solving that rational expression, but any assistance in figuring it out would be greatly appreciated. :] Thank you guys for your time.

    Colton
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  2. #2
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    Jan 2010
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    Hint:

    $\displaystyle x^2-y^2 = (x+y)(x-y)$
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  3. #3
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    Nov 2009
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    California, United States
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    fishcake,

    Thank you for your hint. That I already knew, but I took a closer look at what I was doing and thought more about it and realized I was simplifying incorrectly. I've figured out what I must do now and have learned as a result of it. Thank you anyway, I appreciate that you took the time to aid me. :]

    Colton
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  4. #4
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    U.S
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    Quote Originally Posted by Noegddgeon View Post
    Hello, everybody. I attempted to solve a rational expression which requires division and apparently got the wrong answer. Here's the expression:

    $\displaystyle

    \frac {\frac {x^2 - y^2}{xy}}{\frac {x - y}{y}}

    $

    The steps I followed are as such:

    1. (Turn it into multiplication):

    $\displaystyle

    \frac {x^2 - y^2}{xy} * \frac {y}{x - y}

    $

    $\displaystyle

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

    $

    2. Multiply:

    $\displaystyle

    \frac {yx^2 - y^3}{yx^2 - xy^2}

    $

    3. Simplify:

    $\displaystyle

    \frac {y}{x}

    $

    However, I checked the answer and apparently it's:

    $\displaystyle

    \frac {x + y}{x}

    $

    I'm not sure what exactly I did wrong in solving that rational expression, but any assistance in figuring it out would be greatly appreciated. :] Thank you guys for your time.

    Colton
    For the record: (I don't like unsolved requests)

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

    1. Cancel out (x-y) because its quotient is 1. It leaves you:

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

    2. Divide out y because its quotient is 1. It leaves you:

    $\displaystyle \frac {x+y} {x}$
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