\( \frac{x}{x^{2}-2 x-24}-\frac{x}{x^{2}-8 x+12}=\square \) (Simplify your answer.)

To simplify the expression \( \frac{x}{x^{2}-2 x-24} - \frac{x}{x^{2}-8 x+12} \), we first factor the denominators. 1. **Factor the first denominator:** \( x^2 - 2x - 24 = (x - 6)(x + 4) \) 2. **Factor the second denominator:** \( x^2 - 8x + 12 = (x - 6)(x - 2) \) Now, we rewrite the expression: \[ \frac{x}{(x - 6)(x + 4)} - \frac{x}{(x - 6)(x - 2)} \] Next, we put it over a common denominator, which is \( (x - 6)(x + 4)(x - 2) \): \[ \frac{x(x - 2) - x(x + 4)}{(x - 6)(x + 4)(x - 2)} \] Now we simplify the numerator: \[ x(x - 2) - x(x + 4) = x^2 - 2x - (x^2 + 4x) = x^2 - 2x - x^2 - 4x = -6x \] So the entire expression becomes: \[ \frac{-6x}{(x - 6)(x + 4)(x - 2)} \] Thus, the simplified answer is: \[ \frac{-6x}{(x - 6)(x + 4)(x - 2)} \]