Simplify ((x-4)/(2x^2))÷((2x+3)/(x+4))

$\frac{x - 4}{2 x^{2}} \div \frac{2 x + 3}{x + 4}$

To divide by a fraction, multiply by its reciprocal.

$\frac{x - 4}{2 x^{2}} \cdot \frac{x + 4}{2 x + 3}$