To determine which of the given expressions is equivalent to [tex]\(\frac{-48 x - 8}{8 x - 64}\)[/tex], we can follow these steps:
### Step 1: Factor both the numerator and the denominator
1. Numerator: [tex]\(-48x - 8\)[/tex]
- Factor out the greatest common factor (GCF). Here, the GCF is [tex]\(-8\)[/tex]:
[tex]\[
-48x - 8 = -8 (6x + 1)
\][/tex]
2. Denominator: [tex]\(8x - 64\)[/tex]
- Factor out the GCF, which is [tex]\(8\)[/tex]:
[tex]\[
8 x - 64 = 8 (x - 8)
\][/tex]
### Step 2: Rewrite the fraction with the factored numerator and denominator
[tex]\[
\frac{-48 x - 8}{8 x - 64} = \frac{-8 (6 x + 1)}{8 (x - 8)}
\][/tex]
### Step 3: Simplify the fraction
- Notice that the [tex]\(8\)[/tex] in the denominator and the [tex]\(-8\)[/tex] in the numerator can be canceled out:
[tex]\[
\frac{-8 (6 x + 1)}{8 (x - 8)} = \frac{-(6 x + 1)}{x - 8}
\][/tex]
- Simplifying this gives:
[tex]\[
\frac{-6 x - 1}{x - 8}
\][/tex]
### Conclusion
The equivalent expression to [tex]\(\frac{-48 x - 8}{8 x - 64}\)[/tex] is [tex]\(\frac{-6 x - 1}{x - 8}\)[/tex].
Thus, the correct answer is:
(C) [tex]\(\frac{-6 x - 1}{x - 8}\)[/tex]
