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

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

To divide by a fraction, multiply by its reciprocal.

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