Subtract. \( \frac{\frac{x}{x^{2}-2 x-15}-\frac{x}{x^{2}-11 x+30}}{\frac{x}{x^{2}-2 x-15}-\frac{x}{x^{2}-11 x+30}=\square \text { (Simplify your answer.) }} \)

To simplify the expression, first let's find a common denominator for the two fractions in the numerator. The denominators are: 1. \(x^{2} - 2x - 15 = (x - 5)(x + 3)\) 2. \(x^{2} - 11x + 30 = (x - 6)(x - 5)\) Now, the common denominator will be the product of the distinct factors from both denominators: \[ (x - 5)(x + 3)(x - 6) \] Now we need to rewrite both fractions over this common denominator. 1. For \( \frac{x}{(x-5)(x+3)} \): \[ \frac{x \cdot (x-6)}{(x-5)(x+3)(x-6)} = \frac{x(x-6)}{(x-5)(x+3)(x-6)} \] 2. For \( \frac{x}{(x-6)(x-5)} \): \[ \frac{x \cdot (x+3)}{(x-6)(x-5)(x+3)} = \frac{x(x+3)}{(x-5)(x+3)(x-6)} \] Now we can combine the fractions in the numerator: \[ \frac{x(x-6) - x(x+3)}{(x - 5)(x + 3)(x - 6)} \] Next, we simplify the numerator: \[ x(x-6) - x(x+3) = x^2 - 6x - x^2 - 3x = -9x \] So, now we have: \[ \frac{-9x}{(x - 5)(x + 3)(x - 6)} \] Thus, the final simplified result is: \[ \frac{-9x}{(x - 5)(x + 3)(x - 6)} \]