# How do you simplify (x-3)/(2x-8)*(6x^2-96)/(x^2-9)?

Feb 18, 2017

$\frac{3 \left(x + 4\right)}{x + 3}$

#### Explanation:

$\frac{x - 3}{2 x - 8} \cdot \frac{6 {x}^{2} - 96}{{x}^{2} - 9}$

factor out anything is able to be factored
$\frac{x - 3}{2 \left(x - 4\right)} \cdot \frac{6 \left({x}^{2} - 16\right)}{\left(x - 3\right) \left(x + 3\right)} = \frac{x - 3}{2 \left(x - 4\right)} \cdot \frac{6 \left(x - 4\right) \left(x + 4\right)}{\left(x - 3\right) \left(x + 3\right)}$

divide out the common factors
$\frac{\cancel{x - 3}}{2 \left(\cancel{x - 4}\right)} \cdot \frac{6 \left(\cancel{x - 4}\right) \left(x + 4\right)}{\left(\cancel{x - 3}\right) \left(x + 3\right)} = \frac{6 \left(x + 4\right)}{2 \left(x + 3\right)} = \frac{3 \left(x + 4\right)}{x + 3}$

To simplify these kinds of problems, just try and factor out anything you see that is able to be factored. You need to get in the habit of just working out the problem even though you don't know what's going to happen next. Many times there are common factors that you can just divide out.