\(P=\left(\frac{x+2}{2x-4}+\frac{x-2}{2x+4}-\frac{8}{x^2-4}\right):\frac{4}{x-2}\)
\(\Rightarrow P=\left[\frac{\left(x+2\right)^2}{2\left(x^2-4\right)}+\frac{\left(x-2\right)^2}{2\left(x^2-4\right)}-\frac{16}{2\left(x^2-4\right)}\right]:\frac{4}{x-2}\)
\(\Rightarrow P=\left(\frac{x^2+4x+4+x^2-4x+4-16}{2\left(x^2-4\right)}\right).\frac{x-2}{4}\)
\(\Rightarrow P=\frac{2x^2-8}{2\left(x^2-4\right)}.\frac{x-2}{4}\)
\(\Rightarrow P=\frac{x-2}{4}\)