Final answer:
Jesse's final answer after factoring the numerator and denominator is (x+3)/7.
Explanation:
In order to reduce the given expression to its lowest terms, Jesse first factored the numerator and denominator separately. This is a common technique used in simplifying fractions. By factoring, we mean expressing the given expression as a product of its factors. In this case, the numerator 3x^2-9x can be factored as 3x(x-3) and the denominator 7x-21 can be factored as 7(x-3).
Next, Jesse noticed that both the numerator and denominator have a common factor of (x-3). By dividing both the numerator and denominator by this common factor, we can cancel it out and simplify the expression further. This is known as cancelling out or reducing.
Therefore, after cancelling out the common factor of (x-3), we are left with (3x)/(7). This is the simplified version of the given expression. However, the question asks for the expression to be reduced to its lowest terms. In this case, we can further simplify the expression by dividing both the numerator and denominator by 3. This gives us the final answer of (x+3)/7.
In summary, Jesse's final answer is (x+3)/7. In this expression, the numerator represents the sum of the product of 3 and x, and 3. This can be written as 3(x+1) or (x+3). Since we do not know the value of x, we cannot simplify this further. The denominator represents the product of 7 and x. Therefore, the final answer is the simplified version of the given expression, written in its lowest terms.