If you divide 2X/3 by 5/X, what is the result?

To find the result of dividing ( \frac{2X}{3} ) by ( \frac{5}{X} ), you start by rewriting the division as multiplication by the reciprocal. Thus, you can express the operation as:

[

\frac{2X}{3} \div \frac{5}{X} = \frac{2X}{3} \times \frac{X}{5}

]

When multiplying these fractions, you multiply the numerators together and the denominators together:

[

\text{Numerator: } 2X \times X = 2X^2

]

[

\text{Denominator: } 3 \times 5 = 15

]

This gives:

[

\frac{2X^2}{15}

]

Therefore, the result of dividing ( \frac{2X}{3} ) by ( \frac{5}{X} ) is indeed ( \frac{2X^2}{15} ). This aligns with option C.

The other answers do not match this calculation. They contain different algebraic forms or coefficients which do not arise from the proper operation on the original fractions. Thus, option