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Math Help - Equation Simplification

  1. #1
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    Equation Simplification

    4x^2-9
    (2x^3)+(3x^2)+8x+12


    Anyone know how to simplify this equation?
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  2. #2
    Super Member 11rdc11's Avatar
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    Does it look like this?

    \frac{4x^2-9}{2x^3} +3x^2 + 8x + 12
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  3. #3
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    4x^2-9_____________
    2x^3+3x^2+8x+12


    oh sorry, the top is over everything
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  4. #4
    Moo
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    Hello,
    Quote Originally Posted by gearshifter View Post
    4x^2-9_____________
    2x^3+3x^2+8x+12


    oh sorry, the top is over everything
    Note that 4x^2-9=(2x)^2-3^2. This is the difference of two squares. (the formula is a^2-b^2=(a-b)(a+b)

    For the denominator, I'm sorry to say it's just a eyeballing...

    2x^3+3x^2+8x+12={\color{red}2}x^3+{\color{blue}3}x  ^2+{\color{red}2}\cdot 4x+{\color{blue}3} \cdot 4)

    Now, you can see some interesting things. If not yet, group the terms with a common factor.

    =2(x^3+4x)+3(x^2+4)

    Factor x in the first term :

    =2x(x^2+4)+3(x^2+4)

    Do you see it ? The factorisation of the denominator ?
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