Thread: How do I simplify this type of expression?

1. How do I simplify this type of expression?

I need help simplifying an expression that is in this form:

(3x + 12) / (9x^2 - 144)

2. Originally Posted by jenbones
I need help simplifying an expression that is in this form:

(3x + 12) / (9x^2 - 144)

Hint: $\displaystyle 9x^2-144= (3x)^2-(12)^2$

Do you know how to factor this?

3. No, I am not very good at factoring.

4. Originally Posted by jenbones
No, I am not very good at factoring.
Remember the difference of squares formula? $\displaystyle a^2-b^2=(a+b)(a-b)$

5. yes, I remember that formula.

6. Originally Posted by jenbones
yes, I remember that formula.
Utilising it will allow you to simplify by cancelling the numerator with one of the factors.

7. Originally Posted by jenbones
I need help simplifying an expression that is in this form:

(3x + 12) / (9x^2 - 144)

$\displaystyle \frac{3x + 12}{9x^2 - 144} = \frac{3x + 12}{(3x+12)(3x-12)} = \frac{1}{3x-12}$
$\displaystyle \frac{3x + 12}{9x^2 - 144} = \frac{3x + 12}{(3x+12)(3x-12)} = \frac{1}{3x-12}$
$\displaystyle \displaystyle\frac{1}{3x-12}=\frac{1}{3(x)-3(4)}=\frac{1}{3(x)+3(-4)}=\frac{1}{3(x-4)}$