Simplify ((x+4)/(x^2+2))÷((x^2-2)/(x-8))

$\frac{x + 4}{x^{2} + 2} \div \frac{x^{2} - 2}{x - 8}$

To divide by a fraction, multiply by its reciprocal.

$\frac{x + 4}{x^{2} + 2} \cdot \frac{x - 8}{x^{2} - 2}$