\[\frac{5x - 10}{2x + 3}\ :\frac{x^{2} - 4}{4x + 6} =\]
\[= \frac{5(x - 2)}{2x + 3} \cdot \frac{4x + 6}{x^{2} - 4} =\]
\[= \frac{5(x - 2) \cdot 2(2x + 3)}{(2x + 3)(x - 2)(x + 2)} =\]
\[= \frac{10}{x + 2}.\]