Description for Correct answer:
The factors of \( \Large x^{2}-4 = \left(x+2\right) \left(x-2\right) \)

The factors of \( \Large x^{3}-8 = \left(x-2\right) \left(x^{2}+2x+4\right) \)

\( \Large \frac{ \left(x^{2}-4\right) \left(x^{3}-8\right) }{ \left(x-2\right)^{2} \left(x^{2}+2x+4\right) } = \frac{ \left(x+2\right) \left(x-2\right) \left(x-2\right) \left(x^{2}+2x+4\right) }{ \left(x-2\right)^{2} \left(x^{2}+2x+4\right) } \)

= \( \Large \left(x+2\right) \)