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

\(=\left[\frac{x\left(x+2\right)}{\left(x-2\right)\left(x+2\right)}-\frac{4}{\left(x-2\right)\left(x+2\right)}\right].\frac{x+2}{x}\)

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

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