Subtract. \[ \frac{x}{x^{2}-4 x-12}-\frac{6}{x^{2}-4 x-12} \] Simplify your answer as much as possible.

To simplify the expression \[ \frac{x}{x^{2}-4x-12}-\frac{6}{x^{2}-4x-12}, \] we first notice that both fractions have the same denominator, \( x^{2} - 4x - 12 \). We can combine the two fractions: \[ \frac{x - 6}{x^{2} - 4x - 12}. \] Next, we will simplify the denominator. We can factor the quadratic \(x^{2} - 4x - 12\). We look for two numbers that multiply to -12 and add to -4. These numbers are -6 and 2. Therefore, we can factor the denominator as follows: \[ x^{2} - 4x - 12 = (x - 6)(x + 2). \] Now, we substitute this factored form into our expression: \[ \frac{x - 6}{(x - 6)(x + 2)}. \] Assuming \(x \neq 6\) to avoid division by zero, we can cancel out the \(x - 6\) term in the numerator and denominator: \[ \frac{1}{x + 2}, \quad \text{for } x \neq 6. \] Therefore, the simplified result is \[ \boxed{\frac{1}{x + 2}} \quad \text{for } x \neq 6. \]