Bài giải:

$\frac{x}{x-2y}+\frac{x}{x+2y}+\frac{4xy}{4{{y}^{2}}-{{x}^{2}}}$= $\frac{x}{x-2y}+\frac{x}{x+2y}+\frac{-4xy}{(x-2y)(x+2y)}$

= $\frac{x(x+2y)}{(x+2y)(x-2y)}+\frac{x(x-2y)}{(x+2y)(x-2y)}+\frac{-4xy}{(x-2y)(x+2y)}$

= $\frac{{{x}^{2}}+2xy+{{x}^{2}}-2xy-4xy}{(x-2y)(x+2y)}$ = $\frac{2{{x}^{2}}-4xy}{(x-2y)(x+2y)}$ = $\frac{2x(x-2y)}{(x-2y)(x+2y)}$ = $\frac{2x}{x+2y}$

Vậy đáp án đúng là: C