# Math Help - Equation Simplification

1. ## Equation Simplification

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

Anyone know how to simplify this equation?

2. Does it look like this?

$\frac{4x^2-9}{2x^3} +3x^2 + 8x + 12$

3. 4x^2-9_____________
2x^3+3x^2+8x+12

oh sorry, the top is over everything

4. Hello,
Originally Posted by gearshifter
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 ?