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Thread: Simplifying rational expressions

  1. #1
    ayanami_00
    Guest

    Simplifying rational expressions

    3x^2-5x-2
    -----------------
    6x^3+2x^2+3x+1'


    k. I simplified it down to this but i couldn't go any further.

    (3x-1)(x+2)
    --------------------
    (6x^3+2x^2)+(3x+1)



    Thanks for the help in advance.
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  2. #2
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    Quote Originally Posted by ayanami_00
    3x^2-5x-2
    -----------------
    6x^3+2x^2+3x+1'


    k. I simplified it down to this but i couldn't go any further.

    (3x-1)(x+2)
    --------------------
    (6x^3+2x^2)+(3x+1)



    Thanks for the help in advance.
    The numerator becomes,
    $\displaystyle (3x+1)(x-2)$

    The denominator can be re-grouped as,
    $\displaystyle 3x(2x^2+1)+(2x^2+1)$ thus,
    $\displaystyle (3x+1)(2x^2+1)$

    Thus, you have,
    $\displaystyle \frac{(3x+1)(x-2)}{(3x+1)(2x^2+1)}$
    Thus,
    $\displaystyle \frac{x-2}{2x^2+1}$
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