Bài giải:

$\frac{4}{x+2}+\frac{3}{x-2}+\frac{5x+2}{4-{{x}^{2}}}$

=$\frac{4}{2+x}+\frac{-3}{2-x}+\frac{5x+2}{\left( 2+x \right)\left( 2-x \right)}$

=$\frac{4\left( 2-x \right)-3\left( 2+x \right)+5x+2}{\left( 2+x \right)\left( 2-x \right)}$

=$\frac{8-4x-6-3x+5x+2}{\left( 2+x \right)\left( 2-x \right)}$

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

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

=$\frac{2}{2+x}$

Đáp án đúng là A