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Math Help - You have to take a look

  1. #1
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    You have to take a look

    Well...here is the original problem:

    2+\frac{3}{2x+1}


    ...and my aproach:

    2+\frac{3}{2x+1}

    = \frac{2}{1}+\frac{3}{2x+1}

    Now the lowest common factor would be 2x+1 and we rewrite the expression as:

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

    Which is the same as:

    = \frac{4x+2+3}{2x+1}

    And finally I have:

    = \frac{4x+5}{2x+1}

    Now my questions is Can this expression be further simplified? As I see we could still make 4x and 2x compensate to obtain

    = \frac{2x+5}{1}

    = 2x+5

    but the book I'm working with states the solution is just

    \frac{4x+5}{2x+1}

    Could it be that simplification works when numerator and denominator imply multiplication only? Mmm...
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  2. #2
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    Quote Originally Posted by Alienis Back View Post
    Well...here is the original problem:

    2+\frac{3}{2x+1}


    ...and my aproach:

    2+\frac{3}{2x+1}

    = \frac{2}{1}+\frac{3}{2x+1}

    Now the lowest common factor would be 2x+1 and we rewrite the expression as:

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

    Which is the same as:

    = \frac{4x+2+3}{2x+1}

    And finally I have:

    = \frac{4x+5}{2x+1}

    Now my questions is Can this expression be further simplified? As I see we could still make 4x and 2x compensate to obtain

    = \frac{2x+5}{1}

    = 2x+5

    but the book I'm working with states the solution is just

    \frac{4x+5}{2x+1}

    Could it be that simplification works when numerator and denominator imply multiplication only? Mmm...
    bingo!
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  3. #3
    Junior Member
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    Apr 2009
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    Montréal
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    It cannot be simplified after you reach \frac {4x+5}{2x+1} because they're followed by an addition and not by a multiplication.
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