Final answer:
The domain of the rational function (x-3)/(x²+9) is the set of all real numbers because there are no x-values that will force the denominator of the function to become zero.
Step-by-step explanation:
To find the domain of the rational function (x-3)/(x²+9), you look for values of x that would cause the denominator to become zero because division by zero is undefined in mathematics. The denominator of the mentioned function is x²+9. However, for any real value of x, x²+9 cannot equal 0 because x² is always a nonnegative number and 9 is a positive number, and adding them will not yield zero. Therefore, there are no restrictions on x. So, the domain of the function is the set of all real numbers.
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