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Math Help - Rational equation with two solutions

  1. #1
    Senior Member vaironxxrd's Avatar
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    Rational equation with two solutions

    Problem:
    \frac{5x}{x-1}-3=\frac{2x+5}{x^2-1}


    Solution
    x=2
    x=-\frac{1}{2}
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  2. #2
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    Re: Rational equation with two solutions

    Quote Originally Posted by vaironxxrd View Post
    Problem:
    \frac{5x}{x-1}-3=\frac{2x+5}{x^2-1}


    Solution
    x=2
    x=-\frac{1}{2}
    \frac{5x}{x-1}-3=\frac{2x+5}{x^2-1}

    common denominator ...

    \frac{5x(x+1)}{(x-1)(x+1)}-\frac{3(x^2-1)}{x^2-1}=\frac{2x+5}{x^2-1}

    numerators form the equation ...

    5x(x+1) - 3(x^2-1) = 2x+5 \, \, ; \, \, x \ne \pm 1

    take it from here?
    Last edited by skeeter; March 15th 2012 at 12:29 PM.
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  3. #3
    Senior Member vaironxxrd's Avatar
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    Re: Rational equation with two solutions

    Quote Originally Posted by skeeter View Post
    \frac{5x}{x-1}-3=\frac{2x+5}{x^2-1}

    common denominator ...

    \frac{5x(x+1)}{(x-1)(x+1)}-\frac{3(x^2-1)}{x^2-1}=\frac{2x+5}{x^2-1}

    numerators form the equation ...

    5x(x+1) - 3(x^2-1) = 2x-5 \, \, ; \, \, x \ne \pm 1

    take it from here?
    I had a very similar equation, though I have 2x+5 at the end.
    I cannot understand why was 2x+5 switched to 2x-5
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  4. #4
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    Re: Rational equation with two solutions

    typo
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  5. #5
    Senior Member vaironxxrd's Avatar
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    Re: Rational equation with two solutions

    Quote Originally Posted by skeeter View Post
    typo
    2x^2+3x-2=0

    (x+2)(2x-1)

    x = -2
    &
    x = 1/2
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