# Math Help - Algebraic Fractions?

1. ## Algebraic Fractions?

Hi,

I have an equation i cannot work out. The question is simplify the following :

(equation in image)

Thanks.

2. ## Re: Algebraic Fractions?

Hello, jeremyjezzanba!

First of all, it is not an equation . . . It's an expression.

Second, exactly where is your difficulty?
. . You don't understand division?
. . You don't know how to factor?
. . You don't know how to reduce?

$\text{Simplify: }\:\frac{x^2-4}{x^2-9} \div \frac{4x+8}{12x-36}$

$\frac{x^2-4}{x^2-9} \div \frac{4x+8}{12x-36} \;=\;\frac{x^2-4}{x^2-9} \cdot \frac{12x-36}{4x+8}$

. . . . . . . . . . . . . $=\;\frac{(x-2)(x+2)}{(x-3)(x+3)}\cdot\frac{12(x-3)}{4(x+2)}$

. . . . . . . . . . . . . $=\;\frac{(x-2)({\color{red}\rlap{/////}}{x+2})}{({\color{blue}\rlap{/////}}x-3)(x+3)}\cdot\frac{{\color{green}\rlap{//}}12^3({\color{blue}\rlap{/////}}x-3)}{{\color{green}\rlap{/}}4({\color{red}\rlap{/////}}x+2)}$

. . . . . . . . . . . . . $=\;\frac{3(x-2)}{x+3}$