Absolutely, let's solve the given expression step by step.
We need to evaluate the expression:
[tex]\[
\frac{7^2}{x^2 - 2}
\][/tex]
for [tex]\(x = 3\)[/tex].
Step 1: Calculate [tex]\(7^2\)[/tex]
First, let's handle the numerator:
[tex]\[
7^2 = 49
\][/tex]
Step 2: Calculate [tex]\(x^2 - 2\)[/tex]
Now, for the denominator, substitute [tex]\(x = 3\)[/tex] into [tex]\(x^2 - 2\)[/tex]:
[tex]\[
3^2 - 2 = 9 - 2 = 7
\][/tex]
Step 3: Divide the Numerator by the Denominator
Finally, divide the numerator by the denominator:
[tex]\[
\frac{49}{7} = 7
\][/tex]
The value of the expression [tex]\(\frac{7^2}{x^2 - 2}\)[/tex] for [tex]\(x = 3\)[/tex] is [tex]\(\boxed{7}\)[/tex].
