To evaluate the expression [tex]\(\frac{3(x+4)(x+1)}{(x+2)(x-2)}\)[/tex] for [tex]\(x = 4\)[/tex]:
1. Substitute [tex]\(x = 4\)[/tex] into the expression:
[tex]\[
\frac{3(4+4)(4+1)}{(4+2)(4-2)}
\][/tex]
2. Simplify the terms inside the parentheses:
[tex]\[
\frac{3(8)(5)}{(6)(2)}
\][/tex]
3. Calculate the values in the numerator and the denominator:
- Numerator: [tex]\(3 \times 8 \times 5\)[/tex]
[tex]\[
3 \times 8 = 24
\][/tex]
[tex]\[
24 \times 5 = 120
\][/tex]
So, the numerator is 120.
- Denominator: [tex]\(6 \times 2\)[/tex]
[tex]\[
6 \times 2 = 12
\][/tex]
So, the denominator is 12.
4. Form the simplified fraction with the values obtained:
[tex]\[
\frac{120}{12}
\][/tex]
5. Divide to get the final result:
[tex]\[
\frac{120}{12} = 10
\][/tex]
The value of [tex]\(\frac{3(x+4)(x+1)}{(x+2)(x-2)}\)[/tex] when [tex]\(x = 4\)[/tex] is [tex]\(10\)[/tex]. Thus, the correct answer is:
C. [tex]\(10\)[/tex]
