To determine the excluded values for the given expression
[tex]\[
\frac{v+4}{v^2 + 5v + 4}
\][/tex]
we need to find the values of [tex]\( v \)[/tex] that make the denominator [tex]\( v^2 + 5v + 4 \)[/tex] equal to zero.
Step-by-Step Solution:
1. Identify the denominator:
The denominator of the expression is [tex]\( v^2 + 5v + 4 \)[/tex].
2. Set the denominator equal to zero:
To find the values that make the denominator zero, solve the equation:
[tex]\[
v^2 + 5v + 4 = 0
\][/tex]
3. Solve for [tex]\( v \)[/tex]:
This can be factored into:
[tex]\[
(v + 4)(v + 1) = 0
\][/tex]
So, solve for [tex]\( v \)[/tex] by setting each factor equal to zero:
[tex]\[
v + 4 = 0
\][/tex]
[tex]\[
v = -4
\][/tex]
and
[tex]\[
v + 1 = 0
\][/tex]
[tex]\[
v = -1
\][/tex]
Therefore, the excluded values, which are the values of [tex]\( v \)[/tex] that make the denominator zero, are:
[tex]\[
v = -4, -1
\][/tex]
