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Math Help - 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:

    <br /> <br />
\frac {\frac {x^2 - y^2}{xy}}{\frac {x - y}{y}}<br /> <br />

    The steps I followed are as such:

    1. (Turn it into multiplication):

    <br /> <br />
\frac {x^2 - y^2}{xy} * \frac {y}{x - y}<br /> <br />

    <br /> <br />
\frac {y(x^2 - y^2)}{xy(x - y)}<br /> <br />

    2. Multiply:

    <br /> <br />
\frac {yx^2 - y^3}{yx^2 - xy^2}<br /> <br />

    3. Simplify:

    <br /> <br />
\frac {y}{x}<br /> <br />

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

    <br /> <br />
\frac {x + y}{x}<br /> <br />

    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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    Hint:

    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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    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:

    <br /> <br />
\frac {\frac {x^2 - y^2}{xy}}{\frac {x - y}{y}}<br /> <br />

    The steps I followed are as such:

    1. (Turn it into multiplication):

    <br /> <br />
\frac {x^2 - y^2}{xy} * \frac {y}{x - y}<br /> <br />

    <br /> <br />
\frac {y(x^2 - y^2)}{xy(x - y)}<br /> <br />

    2. Multiply:

    <br /> <br />
\frac {yx^2 - y^3}{yx^2 - xy^2}<br /> <br />

    3. Simplify:

    <br /> <br />
\frac {y}{x}<br /> <br />

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

    <br /> <br />
\frac {x + y}{x}<br /> <br />

    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)

    \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:

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

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

    \frac {x+y} {x}
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