How do you simplify and find the excluded values of (x+3)/(x^2+7x+12)?

Feb 16, 2017

See the entire solution process below:

Explanation:

We can factor the denominator as:

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

We can than simplify this expression as:

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{x + 3}}}}{\left(\textcolor{red}{\cancel{\textcolor{b l a c k}{x + 3}}}\right) \left(x + 4\right)} = \frac{1}{x + 4}$

To find the excluded values we need to solve for the denominator equal to $0$:

Exclusion 1)

$x + 3 = 0$

$x + 3 - 3 = 0 - 3$

$x + 0 = - 3$

$x = - 3$

Exclusion 2)

$x + 4 = 0$

$x + 4 - 4 = 0 - 4$

$x + 0 = - 4$

$x = - 4$

The excluded values are $- 3$ and $- 4$