To determine the expression equivalent to [tex]\(\frac{72}{-24z-8}\)[/tex], let's simplify it step-by-step.
First, write the given expression:
[tex]\[
\frac{72}{-24z-8}
\][/tex]
Next, factor the denominator. Observe that both terms in the denominator, [tex]\(-24z\)[/tex] and [tex]\(-8\)[/tex], have a common factor of [tex]\(-8\)[/tex]:
[tex]\[
-24z - 8 = -8(3z + 1)
\][/tex]
Now, substitute this factor back into the expression:
[tex]\[
\frac{72}{-8(3z + 1)}
\][/tex]
We can simplify the fraction by dividing the numerator by [tex]\(-8\)[/tex] and then expressing the result with the simplified denominator:
[tex]\[
\frac{72}{-8(3z + 1)} = \frac{72}{-8} \cdot \frac{1}{3z + 1}
\][/tex]
Simplify [tex]\(\frac{72}{-8}\)[/tex]:
[tex]\[
\frac{72}{-8} = -9
\][/tex]
This simplifies the entire expression to:
[tex]\[
\frac{-9}{3z + 1} = \frac{9}{-3z - 1}
\][/tex]
Putting it all together, we have:
[tex]\[
\frac{72}{-24z - 8} = \frac{9}{-3z - 1}
\][/tex]
So, the equivalent expression is:
[tex]\[
\boxed{\frac{9}{-3z - 1}}
\][/tex]
Hence, the correct answer is:
(B) [tex]\(\frac{9}{-3z-1}\)[/tex]
