To solve the expression [tex]\(\frac{x^2 + 7}{x - 7}\)[/tex] when [tex]\(x = 5\)[/tex], follow these steps:
1. Substitute [tex]\(x = 5\)[/tex] into the expression:
[tex]\[
\frac{5^2 + 7}{5 - 7}
\][/tex]
2. Calculate the numerator:
[tex]\[
5^2 + 7 = 25 + 7 = 32
\][/tex]
3. Calculate the denominator:
[tex]\[
5 - 7 = -2
\][/tex]
4. Divide the numerator by the denominator:
[tex]\[
\frac{32}{-2} = -16
\][/tex]
Therefore, the value of the expression when [tex]\(x = 5\)[/tex] is [tex]\(-16\)[/tex].
Finally, the expression evaluates to [tex]\(\boxed{-16}\)[/tex].
