To solve the given problem, we need to simplify the rational expression:
[tex]\[
\frac{x^2 - 16}{x - 4}
\][/tex]
First, notice that the numerator [tex]\(x^2 - 16\)[/tex] can be factored. This is a difference of squares:
[tex]\[
x^2 - 16 = (x + 4)(x - 4)
\][/tex]
So the original expression becomes:
[tex]\[
\frac{(x + 4)(x - 4)}{x - 4}
\][/tex]
Since [tex]\(x \neq 4\)[/tex], we can safely cancel the common factor [tex]\(x - 4\)[/tex] in the numerator and denominator:
[tex]\[
\frac{(x + 4)(x - 4)}{x - 4} = x + 4
\][/tex]
Therefore, the simplified form of the given rational expression is [tex]\(x + 4\)[/tex].
So the correct answer is:
[tex]\[
\boxed{B}
\][/tex]
