Bài giải:

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

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

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

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

=$\frac{4x}{1+{{x}^{2}}}$

Đáp án đúng là C