# How do you find the quotient of (2x+8)/(x+3)div(x+4)/(x^2+6x+9)?

Mar 30, 2017

$2 x + 6$

#### Explanation:

$\frac{2 x + 8}{x + 3} \div \frac{x + 4}{{x}^{2} + 6 x + 9}$

change the sign $\div$ to * ( multiplication) and change the position of $\frac{x + 4}{{x}^{2} + 6 x + 9}$ to $\frac{{x}^{2} + 6 x + 9}{x + 4}$

$= \frac{2 x + 8}{x + 3} \cdot \frac{{x}^{2} + 6 x + 9}{x + 4}$

$= \frac{2 \left(\cancel{x + 4}\right)}{\cancel{\left(x + 3\right)}} \cdot \frac{\left(x + 3\right) \cancel{\left(x + 3\right)}}{\cancel{\left(x + 4\right)}}$

$= 2 \left(x + 3\right) = 2 x + 6$