Bài giải:

$\left( \frac{1}{{{x}^{2}}+4x+4}-\frac{1}{{{x}^{2}}-4x+4} \right):\left( \frac{1}{x+2}+\frac{1}{x-2} \right)$

=$\frac{{{\left( x-2 \right)}^{2}}-{{\left( x+2 \right)}^{2}}}{{{\left[ \left( x+2 \right)\left( x-2 \right) \right]}^{2}}}.\frac{\left( x+2 \right)\left( x-2 \right)}{2x}$

=$\frac{-8x}{{{\left[ \left( x+2 \right)\left( x-2 \right) \right]}^{2}}}.\frac{\left( x-2 \right)\left( x+2 \right)}{2x}$

=$\frac{-4}{{{x}^{2}}-4}$

Đáp án đúng là B