# How do you find the domain and range of f(x) = (x+3 )/ (x^2 + 8x + 15)?

Oct 19, 2015

$x \ne - 3 , - 5$
Or is can be written as $\left(- \infty , - 3\right) \cup \left(- 3 , - 5\right) \cup \left(- 5 , \infty\right)$
you may have been taught to use '[ ]' for included and '] [' for excluding.

#### Explanation:

You need to simplify the denominator and find where x = 0.

${x}^{2} + 8 x + 15$

$\frac{15}{3} = 5$

$\left(x + 3\right) \left(x + 5\right)$

$x + 3 = 0 , x + 5 = 0$

$x = - 3 , x = - 5$

Since the denominator cannot be zero, since $\frac{0}{0} = \text{Err}$,
The domain is $x \ne - 3 , - 5$