Final answer:
To find ((f)/(g))(x), substitute the given functions f(x) = x³ - 27 and g(x) = 3x - 9 into the expression ((f)/(g))(x) = (x³ - 27) / (3x - 9). Simplify the expression using the difference of cubes formula to get ((f)/(g))(x) = (x - 3)(x² + 3x + 9) / 3(x - 3). The (x - 3) term cancels out, leaving ((f)/(g))(x) = (x² + 3x + 9) / 3.
Step-by-step explanation:
To find ((f)/(g))(x), we need to substitute the given functions f(x) = x³ - 27 and g(x) = 3x - 9 into the expression. So, ((f)/(g))(x) = (x³ - 27) / (3x - 9).
Simplifying further, we can factor out x³ - 27 using the difference of cubes formula: ((f)/(g))(x) = ((x - 3)(x² + 3x + 9)) / (3x - 9).
Therefore, ((f)/(g))(x) = (x - 3)(x² + 3x + 9) / 3(x - 3). The (x - 3) term cancels out, leaving ((f)/(g))(x) = (x² + 3x + 9) / 3.
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