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Math Help - Help with Rational Expression

  1. #1
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    Help with Rational Expression

    Hello, everybody. I got the gist of rational expressions I think, at least on a basic level, but I'm having trouble with this particular one:

    \frac {7}{x+2} - \frac {x + 8}{4 - x^2} + \frac {3x - 2}{4 - 4x + x^2}

    The solution I ended up coming with was this:

    \frac {-11x^2 + 10x - 16}{-x^3 + x^2 + 6x + 8}

    However, the actual solution is this, according to the solutions portion of the text I'm learning from:

    \frac {11x^2 - 18x + 8}{(2 + x)(2 - x)^2}

    I came up with my "solution" by finding the LCD by factoring every denominator of the three fractional operands and then multiplying them all by each other, then multiplying the numerators by those missing pieces of the factored denominators from the other operands. Then, I tried to simplify everything down, but I think I screwed up somewhere. I would greatly appreciate if someone could help me out by either giving me a set of instructions or showing the process of solving this problem step-by-step. :] Thanks a lot in advance.

    Colton
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  2. #2
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    Quote Originally Posted by Noegddgeon View Post
    Hello, everybody. I got the gist of rational expressions I think, at least on a basic level, but I'm having trouble with this particular one:

    \frac {7}{x+2} - \frac {x + 8}{4 - x^2} + \frac {3x - 2}{4 - 4x + x^2}

    The solution I ended up coming with was this:

    \frac {-11x^2 + 10x - 16}{-x^3 + x^2 + 6x + 8}

    However, the actual solution is this, according to the solutions portion of the text I'm learning from:

    \frac {11x^2 - 18x + 8}{(2 + x)(2 - x)^2}

    I came up with my "solution" by finding the LCD by factoring every denominator of the three fractional operands and then multiplying them all by each other, then multiplying the numerators by those missing pieces of the factored denominators from the other operands. Then, I tried to simplify everything down, but I think I screwed up somewhere. I would greatly appreciate if someone could help me out by either giving me a set of instructions or showing the process of solving this problem step-by-step. :] Thanks a lot in advance.

    Colton
    All your calculations are OK. I assume that you've made a tiny sign mistake. Please compare your results:

    \frac {7}{x+2} - \frac {x + 8}{4 - x^2} + \frac {3x - 2}{4 - 4x + x^2} =  \frac {7}{x+2} + \frac {x + 8}{x^2-4} + \frac {3x - 2}{4 - 4x + x^2} =  ~~\frac {7x^2-28x+28+x^2+8x-2x-16+3x^2+6x-2x-4}{(x+2)(x-2)^2}
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  3. #3
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    Earboth,

    Thank you for your reply. It looks like you're correct; my mistake. haha I appreciate the help and I hope I don't run into any more mistakes like that again.

    Colton
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