We are asked to evaluate the limit of the expression $\frac{x-4}{x^2 - 16}$ as $x$ approaches 4.

1. Problem Description

We are asked to evaluate the limit of the expression $\frac{x-4}{x^2 - 16}$ as $x$ approaches

4.

2. Solution Steps

We need to evaluate the limit:

$\lim_{x \to 4} \frac{x-4}{x^2 - 16}$

First, we can factor the denominator:

$x^2 - 16 = (x-4)(x+4)$

So the expression becomes:

$\lim_{x \to 4} \frac{x-4}{(x-4)(x+4)}$

We can cancel the $(x-4)$ terms, as long as $x \neq 4$:

$\lim_{x \to 4} \frac{1}{x+4}$

Now, we can substitute $x = 4$ into the expression:

$\frac{1}{4+4} = \frac{1}{8}$

3. Final Answer

The limit is $\frac{1}{8}$.