Simplify \((\frac{3}{x} + \frac{15}{2y}) \div \frac{6}{xy}\)

A.

\(\frac{2y - 5x}{4}\)

B.

\(\frac{9(2x - 5x)}{x^2y^2}\)

C.

\(\frac{5x - 2y}{2}\)

D.

\(\frac{c^2y^2}{18y - 45x}\)

E.

\(\frac{4}{2y - 5x}\)

Correct answer is A

\((\frac{3}{x} - \frac{15}{2y}) \div \frac{6}{xy}\)

= \((\frac{6y - 15x}{2xy}) \div \frac{6}{xy}\)

= \(\frac{6y - 15x}{2xy} \times \frac{xy}{6}\)

= \(\frac{3(2y - 5x)}{2xy} \times \frac{xy}{6}\)

= \(\frac{2y - 5x}{4}\)