To evaluate the expression [tex]\(\frac{z^2 - 4x}{x}\)[/tex] when [tex]\(x = 3\)[/tex] and [tex]\(z = 6\)[/tex], follow these step-by-step instructions:
1. Substitute the given values of [tex]\(x\)[/tex] and [tex]\(z\)[/tex] into the expression:
[tex]\[
\frac{6^2 - 4 \cdot 3}{3}
\][/tex]
2. Calculate [tex]\(z^2\)[/tex]:
[tex]\[
6^2 = 36
\][/tex]
3. Calculate [tex]\(4x\)[/tex]:
[tex]\[
4 \cdot 3 = 12
\][/tex]
4. Subtract [tex]\(4x\)[/tex] from [tex]\(z^2\)[/tex]:
[tex]\[
36 - 12 = 24
\][/tex]
5. Use the result as the numerator and substitute back into the expression:
[tex]\[
\frac{24}{3}
\][/tex]
6. Simplify the expression:
[tex]\[
\frac{24}{3} = 8.0
\][/tex]
Therefore, the simplified result is [tex]\(\boxed{8.0}\)[/tex].
Additionally, if we describe the intermediate results:
- The numerator of the expression [tex]\(z^2 - 4x\)[/tex] is [tex]\(24\)[/tex].
- The denominator of the expression is [tex]\(3\)[/tex].
So, putting it all together:
[tex]\[
\frac{24}{3} = 8.0
\][/tex]
This leads us to a final answer of [tex]\(\boxed{8.0}\)[/tex].
