Final answer:
The domain of the rational function R(x)=8(x²-4x-12) / 9(x²-36) is all real numbers except x=-6 and x=6.
Step-by-step explanation:
The domain of a rational function is the set of all real numbers except the values of x that would make the denominator equal to zero. In this case, the denominator is 9(x²-36), which equals zero when x²-36 equals zero. To find the values of x that make the denominator zero, we solve the equation x²-36=0:
x²=36
x=±√(36)
Therefore, the domain of the rational function R(x)=8(x²-4x-12) / 9(x²-36) is all real numbers except x=-6 and x=6.