\(A=\dfrac{x-2}{x+2}-\dfrac{x}{x-2}-\dfrac{9x+2}{4-x^2}\)
\(=\dfrac{\left(x-2\right)^2}{x^2-4}-\dfrac{x\left(x+2\right)}{x^2-4}+\dfrac{9x+2}{x^2-4}\)
\(=\dfrac{x^2-4x+4-x^2-2x+9x+2}{x^2-4}\)
\(=\dfrac{3x+6}{x^2-4}\)
\(=\dfrac{3\left(x+2\right)}{\left(x-2\right)\left(x+2\right)}\)
\(=\dfrac{3}{x-2}\) ( đpcm )