# Equation Simplification

• Sep 18th 2008, 10:03 AM
gearshifter
Equation Simplification
4x^2-9
(2x^3)+(3x^2)+8x+12

Anyone know how to simplify this equation?
• Sep 18th 2008, 10:11 AM
11rdc11
Does it look like this?

$\displaystyle \frac{4x^2-9}{2x^3} +3x^2 + 8x + 12$
• Sep 18th 2008, 10:13 AM
gearshifter
4x^2-9_____________
2x^3+3x^2+8x+12

oh sorry, the top is over everything
• Sep 18th 2008, 10:20 AM
Moo
Hello,
Quote:

Originally Posted by gearshifter
4x^2-9_____________
2x^3+3x^2+8x+12

oh sorry, the top is over everything

Note that $\displaystyle 4x^2-9=(2x)^2-3^2$. This is the difference of two squares. (the formula is $\displaystyle a^2-b^2=(a-b)(a+b)$

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

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

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

$\displaystyle =2(x^3+4x)+3(x^2+4)$

Factor x in the first term :

$\displaystyle =2x(x^2+4)+3(x^2+4)$ (Surprised)

Do you see it ? The factorisation of the denominator ?