Final answer:
The equivalent expression to (f(x))/(g(x)), for x > 3, is x(x + 3)/(x + 1), obtained by factoring and simplifying the given functions f(x) and g(x).
Step-by-step explanation:
The question asks which expression is equivalent to (f(x))/(g(x)) given:
- f(x) = x³ - 9x
- g(x) = x² - 2x - 3
For x > 3, we need to simplify the expression (x³ - 9x) / (x² - 2x - 3). To simplify this, we factor both the numerator and the denominator:
Numerator: x³ - 9x = x(x² - 9) = x(x + 3)(x - 3)
Denominator: x² - 2x - 3 can be factored as (x - 3)(x + 1)
Then the expression becomes:
(x(x + 3)(x - 3)) / ((x - 3)(x + 1))
Since x > 3, x - 3 is not equal to zero and can be cancelled out:
(x(x + 3)) / (x + 1)
Thus, the equivalent expression is x(x + 3)/(x + 1) for x > 3.