To determine which of the given choices is equal to the rational expression [tex]\(\frac{x^2 - 49}{x - 7}\)[/tex] when [tex]\(x \neq 7\)[/tex], let's follow these steps:
1. Factor the Numerator: Notice that the numerator [tex]\(x^2 - 49\)[/tex] is a difference of squares. We can factor it accordingly:
[tex]\[
x^2 - 49 = (x - 7)(x + 7)
\][/tex]
2. Rewrite the Expression: Substitute the factored form of the numerator back into the expression:
[tex]\[
\frac{x^2 - 49}{x - 7} = \frac{(x - 7)(x + 7)}{x - 7}
\][/tex]
3. Simplify the Expression: Since [tex]\(x \neq 7\)[/tex], the [tex]\(x - 7\)[/tex] terms in the numerator and the denominator are not zero and can be canceled out:
[tex]\[
\frac{(x - 7)(x + 7)}{x - 7} = x + 7
\][/tex]
Therefore, the rational expression [tex]\(\frac{x^2 - 49}{x - 7}\)[/tex] simplifies to [tex]\(x + 7\)[/tex] when [tex]\(x \neq 7\)[/tex].
Thus, the correct answer is:
[tex]\[
\boxed{B. \ x+7}
\][/tex]
