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Math Help - Rational equations algebraically (quick question)

  1. #1
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    Rational equations algebraically (quick question)

    Solve the following rational equation algebraically.

    x^2/2 = x/(x-1)

    Determine the point(s) of intersection of the following rational function...
    f(x)= (2x+3) / x

    Thanks.
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  2. #2
    GAMMA Mathematics
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    Quote Originally Posted by johett View Post
    Solve the following rational equation algebraically.

    x^2/2 = x/(x-1)

    Determine the point(s) of intersection of the following rational function...
    f(x)= (2x+3) / x

    Thanks.
    \frac{x^2}{2} = \frac{x}{(x-1)}

    (x-1)x^2 = 2x

    x^3-x^2 - 2x = 0

    x^2-x - 2 = 0; Keep in mind x can equal zero!

    (x+1)(x-2) = 0

    x=-1,0,2
    Last edited by colby2152; January 2nd 2008 at 10:58 AM.
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  3. #3
    Math Engineering Student
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    Quote Originally Posted by colby2152 View Post
    x^3-x^2 - 2x = 0

    x^2-x - 2 = 0
    Careful with this step.

    x=0 satisfies the original equation too.
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  4. #4
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    Quote Originally Posted by colby2152 View Post
    \frac{x^2}{2} = \frac{x}{(x-1)}

    (x-1)x^2 = 2x

    x^3-x^2 - 2x = 0

    x^2-x - 2 = 0
    Iso: NO, NO!!If you carelessly divide you will miss x=0 solution!!

    (x+1)(x-2) = 0

    x=-1,2
    Apart from that everything else is perfect
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  5. #5
    GAMMA Mathematics
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    Quote Originally Posted by Krizalid View Post
    Careful with this step.

    x=0 satisfies the original equation too.
    Yeah, the guys caught me going too fast. Even a seasoned vet will make mistakes if the work becomes too sloppy!
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