Final answer:
The restricted domain of the expression 3x - 1 / x² - 9 excludes the values x = -3 and x = 3, where the denominator is zero. Therefore, the domain is all real numbers except x = -3 and x = 3.
Step-by-step explanation:
The student is asking how to find the restricted domain for the rational expression 3x - 1 / x² - 9.
To find the restricted domain, we look for values of x that would make the denominator zero, as division by zero is undefined in mathematics.
The expression in the denominator is x² - 9, which can be factored into (x+3)(x-3). The values that would make this expression zero are x = -3 and x = 3.
Therefore, these values are excluded from the domain of the function.
The domain of the expression is all real numbers except x = -3 and x = 3.
In interval notation, this is represented as (-∞, -3) U (-3, 3) U (3, ∞).