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Math Help - Simplifying expression please help

  1. #1
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    Simplifying expression please help

    Okay so I tried solving it on my own, but I think I did the last step wrong. My answer was not correct. Can anyone show me a step by step answer on how to simplify this expression:

    (3x + 1) / (x + 2) - (-5) / (x + 7)
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  2. #2
    Pim
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    \frac{3x + 1}{x+2}-\frac{-5}{x+7}
    You will want to make the denominators equal, so you multiply the first fraction with \frac{x+7}{x+7} and the second with \frac{x+2}{x+2}

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

    \frac{3x^2+x+21x+7}{(x+2)(x+7)}-\frac{-5x-10}{(x+2)(x+7)}

    \frac{3x^2+22x+7}{(x+2)(x+7)}-\frac{-5x-10}{(x+2)(x+7)}

    \frac{3x^2+27x+17}{(x+2)(x+7)}
    Note that you need to do - (-5x-10) which comes down to +5x+10
    Some people prefer to multiply out the denominator, but I personally don't.
    Does this make it clear?
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  3. #3
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    Quote Originally Posted by Pim View Post
    \frac{3x + 1}{x+2}-\frac{-5}{x+7}
    You will want to make the denominators equal, so you multiply the first fraction with \frac{x+7}{x+7} and the second with \frac{x+2}{x+2}

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

    \frac{3x^2+x+21x+7}{(x+2)(x+7)}-\frac{-5x-10}{(x+2)(x+7)}

    \frac{3x^2+22x+7}{(x+2)(x+7)}-\frac{-5x-10}{(x+2)(x+7)}

    \frac{3x^2+27x+17}{(x+2)(x+7)}
    Note that you need to do - (-5x-10) which comes down to +5x+10
    Some people prefer to multiply out the denominator, but I personally don't.
    Does this make it clear?
    Yes thank you.
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