Final answer:
To divide and simplify the complex fraction (4c)/(5d) divided by (2c²)/(15cd), you multiply by the reciprocal of the second fraction and simplify by canceling common factors, resulting in the simplified form 3c/d.
Step-by-step explanation:
The student's question revolves around the division and simplification of a complex fraction: (4c)/(5d) divided by (2c²)/(15cd). To solve this problem, we can multiply the first fraction by the reciprocal of the second fraction. Doing so, we will have the expression (4c)/(5d) * (15cd)/(2c²).
When simplifying complex fractions, it's important to remember to multiply the numerators together and multiply the denominators together, and then simplify by canceling out any common factors. In our example, we can simplify the numerators by canceling out c and the denominators by canceling c, which leaves us with 2c in the numerator and 5d in the denominator. We can also cancel d from the denominator of the second fraction and numerator of the first fraction to be left with (4 * 15)/(5 * 2), which simplifies to 12.
After simplification, we find the answer to be 3c/d. This completes the division and simplification process for the given complex fraction.