Absolutely, let's simplify the rational expression [tex]\(\frac{6z - 24}{7z - 28}\)[/tex] step-by-step.
1. Factor both the numerator and the denominator:
- For the numerator [tex]\(6z - 24\)[/tex]:
[tex]\[
6z - 24 = 6(z - 4)
\][/tex]
- For the denominator [tex]\(7z - 28\)[/tex]:
[tex]\[
7z - 28 = 7(z - 4)
\][/tex]
2. Rewrite the rational expression using the factored forms:
[tex]\[
\frac{6z - 24}{7z - 28} = \frac{6(z - 4)}{7(z - 4)}
\][/tex]
3. Simplify by cancelling out the common factor [tex]\((z - 4)\)[/tex]:
[tex]\[
\frac{6(z - 4)}{7(z - 4)} = \frac{6}{7} \quad \text{(for } z \neq 4\text{, to avoid division by zero)}
\][/tex]
So, the simplified form of the given rational expression [tex]\(\frac{6z - 24}{7z - 28}\)[/tex] is [tex]\(\frac{6}{7}\)[/tex].
