What is the result of dividing two fractions: (2X/3) ÷ (5/X)?

To find the result of dividing two fractions, you can multiply the first fraction by the reciprocal of the second fraction. In this case, you have (2X/3) divided by (5/X).

First, identify the reciprocal of (5/X), which is (X/5). Then, you multiply the first fraction by this reciprocal:

[

(2X/3) ÷ (5/X) = (2X/3) * (X/5)

]

Next, you can multiply the numerators together and the denominators together:

[

= \frac{2X \cdot X}{3 \cdot 5} = \frac{2X^2}{15}

]

Thus, the result of dividing the two fractions is ( \frac{2X^2}{15} ).

This solution reflects the properties of fraction division, as reversing the second fraction and performing multiplication is a standard method. Other options would not yield this result based on the operations performed, as they do not follow the correct procedure or misinterpret the multiplication or division of the numerator and denominator.