# How do you simplify (x^2 + 8x + 15) /( x - 4) * (x^2 - 16) /( 2x + 6)?

Jul 25, 2015

I found: $\frac{1}{2} \left(x + 5\right) \left(x + 4\right)$

#### Explanation:

You can factorize most of your terms to get:
$\frac{\left(x + 3\right) \left(x + 5\right)}{x - 4} \cdot \frac{\left(x + 4\right) \left(x - 4\right)}{2 \left(x + 3\right)} =$
simplifying:
$= \frac{\cancel{\left(x + 3\right)} \left(x + 5\right)}{\cancel{\left(x - 4\right)}} \frac{\left(x + 4\right) \cancel{\left(x - 4\right)}}{2 \cancel{\left(x + 3\right)}} =$
Finally:
$= \frac{1}{2} \left(x + 5\right) \left(x + 4\right)$