Perform the operation and combine to one fraction. \[ \frac{3 x}{x+4}-\frac{3}{x-8} \]

To combine the fractions, we'll first find a common denominator, which is \((x + 4)(x - 8)\). We rewrite each fraction with this common denominator: \[ \frac{3x}{x+4} = \frac{3x(x-8)}{(x+4)(x-8)} \] \[ \frac{3}{x-8} = \frac{3(x+4)}{(x-8)(x+4)} \] Now, we can rewrite the expression: \[ \frac{3x(x-8) - 3(x+4)}{(x+4)(x-8)} \] Next, we expand both the numerator terms: 1. For \(3x(x-8)\): \[ 3x^2 - 24x \] 2. For \(-3(x+4)\): \[ -3x - 12 \] Putting it all together in the numerator: \[ 3x^2 - 24x - 3x - 12 = 3x^2 - 27x - 12 \] Thus, the combined fraction becomes: \[ \frac{3x^2 - 27x - 12}{(x+4)(x-8)} \] So the final answer is: \[ \frac{3x^2 - 27x - 12}{(x+4)(x-8)} \]