Divide. State the quotient in simplest form, and express the domain of the expression.
(4)/(3x^5) ÷ (12)/(5x^7)
A. (15x^12)/(48), x ≠ 0
B. (5x^2)/(9), x ≠ 0
C. (9)/(5x^2), x ≠ 0
D. (16)/(5x^12), x ≠ 0
To divide two fractions, we need to multiply the first fraction by the reciprocal of the second fraction.
So, to find the quotient of (4)/(3x^5) ÷ (12)/(5x^7), we can rewrite it as (4)/(3x^5) * (5x^7)/(12).
Now, we can simplify the expression by canceling common factors.
In the numerator, we can cancel a factor of 4 with 4 in the denominator, leaving us with 1 in the numerator.
In the denominator, we can cancel a factor of 3 with 12, leaving us with 4 in the numerator.
For the variable factors, we can cancel x^5 with x^7, resulting in x^2 in the numerator.
The simplified expression is (1 * 5x^2)/(4) or (5x^2)/(4).
The domain of the expression is x ≠ 0, since we cannot divide by zero.
Therefore, the correct answer is B. (5x^2)/(9), x ≠ 0.