Answer
$$\frac{x+6}{\left(x-6\right)^2\left(x-2\right)}$$
Work Step by Step
Dividing the two expressions and then cancelling out like terms and factors in the numerator and the denominator, we find:
$$\frac{\frac{x^2+12x+36}{x^2-8x+12}}{x^2-36}\\ \frac{\left(x+6\right)^2}{\left(x-6\right)^2\left(x-2\right)\left(x+6\right)}\\ \frac{x+6}{\left(x-6\right)^2\left(x-2\right)}$$
