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Math Help - Adding Rational Expressions

  1. #1
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    Adding Rational Expressions

    2(4x+1)/5x-7 + 3(x-2)7-5x + -10x -1/5x-7


    The answer in the book is -1. The closest I've come to getting that number is

    5x -3/5x-7

    But obviously that's not write and I had to do some pretty creative things to come up with that number. I'm pretty sure my error is happening when multiplying the middle term by -1 but still, I'm not getting the right answer. Any help is appreciated. Thanks.

    P.S. If there's a way to more easily write out mathematical terms on the computer, I'd like to know about it.
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  2. #2
    Senior Member eumyang's Avatar
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    \dfrac{2(4x+1)}{5x-7} + \dfrac{3(x-2)}{7-5x} + \dfrac{-10x -1}{5x-7}

    You'll need to switch the terms in the denominator of the 2nd fraction and then change the plus in front of the 2nd fraction to a minus:
    =\dfrac{2(4x+1)}{5x-7} - \dfrac{3(x-2)}{5x - 7} + \dfrac{-10x -1}{5x-7}

    =\dfrac{2(4x+1) - 3(x-2) + (-10x -1)}{5x-7}

    =\dfrac{8x + 2 - 3x + 6 - 10x  - 1}{5x-7}

    =\dfrac{-5x + 7}{5x-7}

    =-\dfrac{5x-7}{5x-7}

    =-1
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  3. #3
    A riddle wrapped in an enigma
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    Quote Originally Posted by Ingersoll View Post
    2(4x+1)/5x-7 + 3(x-2)7-5x + -10x -1/5x-7


    The answer in the book is -1. The closest I've come to getting that number is

    5x -3/5x-7

    But obviously that's not write and I had to do some pretty creative things to come up with that number. I'm pretty sure my error is happening when multiplying the middle term by -1 but still, I'm not getting the right answer. Any help is appreciated. Thanks.

    P.S. If there's a way to more easily write out mathematical terms on the computer, I'd like to know about it.

    Hi Ingersoll,

    This is what you have written:

    \frac{2(4x+1)}{5x}-7+3(x-2)7-5x+-10x-\frac{1}{5x}-7

    Apparently eumyang deciphered it, but it is majorly confusing. Use grouping symbols.
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  4. #4
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    I look forward to more of your insightful help in the future. My apologies for leaving you so baffled by inadvertantly leaving out one grouping symbol in a problem with a stated answer and solution.
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  5. #5
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    Quote Originally Posted by Ingersoll View Post
    I look forward to more of your insightful help in the future. My apologies for leaving you so baffled by inadvertantly leaving out one grouping symbol in a problem with a stated answer and solution.

    2(4x+1)/(5x-7) + 3(x-2)/(7-5x) + (-10x -1)/(5x-7)
    ... you left out four grouping symbols and a division sign.
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