# How do you simplify (x^2 - 16 )/( 2x^2 - 9x + 4) div (2x^2 + 14x + 24) /( 4x + 4)?

Aug 9, 2015

$\frac{2 \left(x + 1\right)}{\left(2 x - 1\right) \left(x + 3\right)}$

#### Explanation:

By factoring note that:

(x^2-16)/(2x^2-9x+4)÷(2x^2+14x+24)/(4x+4)=

$\frac{\left(x + 4\right) \left(x - 4\right)}{\left(2 x - 1\right) \left(x - 4\right)} \cdot \frac{4 \left(x + 1\right)}{2 \left(x + 3\right) \left(x + 4\right)}$

Cancel like terms:

$\frac{\cancel{\left(x + 4\right)} \cancel{\left(x - 4\right)}}{\left(2 x - 1\right) \cancel{\left(x - 4\right)}} \cdot \frac{\cancel{4} \textcolor{b l u e}{2} \left(x + 1\right)}{\cancel{2} \left(x + 3\right) \cancel{\left(x + 4\right)}} =$

$\frac{2 \left(x + 1\right)}{\left(2 x - 1\right) \left(x + 3\right)}$