To evaluate the expression [tex]\(\frac{4(x+3)(x+1)}{(x+5)(x-5)}\)[/tex] for [tex]\(x = 3\)[/tex], we can follow these steps:
1. Substitute [tex]\(x = 3\)[/tex] into the expression:
[tex]\[
\frac{4(3+3)(3+1)}{(3+5)(3-5)}
\][/tex]
2. Simplify the values inside the parentheses:
[tex]\[
3 + 3 = 6
\][/tex]
[tex]\[
3 + 1 = 4
\][/tex]
[tex]\[
3 + 5 = 8
\][/tex]
[tex]\[
3 - 5 = -2
\][/tex]
3. Replace these simplified values back into the expression:
[tex]\[
\frac{4 \cdot 6 \cdot 4}{8 \cdot (-2)}
\][/tex]
4. Calculate the numerator:
[tex]\[
4 \cdot 6 = 24
\][/tex]
[tex]\[
24 \cdot 4 = 96
\][/tex]
So, the numerator is [tex]\(96\)[/tex].
5. Calculate the denominator:
[tex]\[
8 \cdot (-2) = -16
\][/tex]
So, the denominator is [tex]\(-16\)[/tex].
6. Form the fraction and simplify:
[tex]\[
\frac{96}{-16} = -6
\][/tex]
Therefore, the value of the expression [tex]\(\frac{4(x+3)(x+1)}{(x+5)(x-5)}\)[/tex] at [tex]\(x = 3\)[/tex] is [tex]\(-6\)[/tex].
The correct answer is:
B. -6
