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Math Help - basic Rational Expression simplifying help

  1. #1
    Junior Member
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    basic Rational Expression simplifying help

    ok so I have the following problem:

    4x+2
    -------- (fraction line, i thought this would be easier)
    12x^2+14x+4

    the answer is 1/3x+2

    I can get pretty close to this but i get stuck along the way

    i end up with:
    2(2x+1)
    -------------
    3x(2x+1)+2(2x+1)

    I dont know what to do, if I cancel out the 2x+1's im still left with a 2 as the numerator, if i cancel out the 2(2x+1) I feel like im breaking a rule because its part of addition (3x+2)

    thanks for any help
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  2. #2
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    Quote Originally Posted by NecroWinter View Post
    ok so I have the following problem:

    4x+2
    -------- (fraction line, i thought this would be easier)
    12x^2+14x+4

    the answer is 1/3x+2

    I can get pretty close to this but i get stuck along the way

    i end up with:
    2(2x+1)
    -------------
    3x(2x+1)+2(2x+1)

    I dont know what to do, if I cancel out the 2x+1's im still left with a 2 as the numerator, if i cancel out the 2(2x+1) I feel like im breaking a rule because its part of addition (3x+2)

    thanks for any help
    note the denominator ... 3x(2x+1)+2(2x+1) = (2x+1)(3x+2)
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  3. #3
    Super Member Quacky's Avatar
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    Windsor, South-East England
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    Edit: Whoops, Skeeter had already answered. Oh well - I'm tired

    Take a factor of 2 out immediately:

    =\displaystyle\frac{2x+1}{6x^2+7x+2}

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