Answer
$$\frac{3x^{2}}{4}$$
Work Step by Step
Dividing by a fraction is equivalent to multiplying by its inverse:
$$\frac{4x}{5}\div \frac{16}{15x}=\frac{4x}{5}\times \frac{15x}{16}=\bigg(\frac{4\times x}{5}\bigg)\times \bigg(\frac{5\times 3\times x}{4\times 4}\bigg).$$
Cancel the common factors $4$ and $5$, and the result is
$$\frac{3x^{2}}{4}.$$
