Simplify the complex fraction. \[ \frac{\frac{x-3}{x^{2}-16}}{1+\frac{1}{x-4}} \]

Step 1 ：Given the complex fraction \(\frac{\frac{x-3}{x^{2}-16}}{1+\frac{1}{x-4}}\)

Step 2 ：First, simplify the denominator. The denominator is a sum of 1 and a fraction. To simplify this, we can find a common denominator and add the fractions. The common denominator is x-4.

Step 3 ：After simplifying the denominator, we will have a fraction divided by another fraction. To simplify this, we can multiply the numerator by the reciprocal of the denominator.

Step 4 ：Finally, we get the simplified form of the complex fraction as \(\boxed{\frac{1}{x+4}}\)