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

Nov 2, 2017

$\text{see explanation}$

#### Explanation:

$\text{the excluded values are the values of x that make}$
$\text{the denominator of the rational function equal zero}$
$\text{as this would make the rational function "color(blue)"undefined}$

$\text{to find the excluded values equate the denominator}$
$\text{to zero and solve for x}$

$\text{solve } {x}^{2} + 7 x + 12 = 0$

$\text{the factors of 12 which sum to + 7 are + 3 and + 4}$

$\Rightarrow \left(x + 3\right) \left(x + 4\right) = 0$

$\text{equate each factor to zero and solve for x}$

$x + 3 = 0 \Rightarrow x = - 3$

$x + 4 = 0 \Rightarrow x = - 4$

$x = - 3 , x = - 4 \leftarrow \textcolor{red}{\text{ are the excluded values}}$

$\text{to simplify "color(blue)"cancel common factors"" on the}$
$\text{numerator/denominator of the rational function}$

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

$= \frac{{\cancel{\left(x + 3\right)}}^{1}}{{\cancel{\left(x + 3\right)}}^{1} \left(x + 4\right)} = \frac{1}{x + 4}$