Multiply as indicated. \[ \frac{x^{2}-36}{x^{2}-2 x-24} \cdot \frac{x+4}{x} \]

To multiply the expression \(\frac{x^{2}-36}{x^{2}-2 x-24} \cdot \frac{x+4}{x}\), we first factor the polynomials in the numerator and denominator. 1. **Factoring the polynomials**: - The expression \(x^2 - 36\) is a difference of squares: \[ x^2 - 36 = (x - 6)(x + 6) \] - The expression \(x^2 - 2x - 24\) can be factored by finding two numbers that multiply to -24 and add to -2, which are -6 and 4: \[ x^2 - 2x - 24 = (x - 6)(x + 4) \] 2. **Rewriting the original expression**: Now we can substitute these factored forms into the multiplication: \[ \frac{(x - 6)(x + 6)}{(x - 6)(x + 4)} \cdot \frac{x + 4}{x} \] 3. **Cancelling common factors**: We can cancel \((x - 6)\) from the numerator and the denominator, and also \((x + 4)\) from the numerator of the second fraction and denominator from the first: \[ = \frac{(x + 6)}{x} \] 4. **Final result**: Thus, the simplified result of the expression is: \[ \frac{x + 6}{x} \] So, the final answer is: \[ \frac{x + 6}{x} \] provided \(x \neq 6\) and \(x \neq -4\) to avoid division by zero.