\(P=\dfrac{x}{2x-4}+\dfrac{x^2}{8-2x^2}\left(x\ne\pm2\right)\)
\(=\dfrac{x}{2\left(x-2\right)}+\dfrac{x^2}{2\left(4-x^2\right)}\)
\(=\dfrac{x}{2\left(x-2\right)}-\dfrac{x^2}{2\left(x-2\right)\left(x+2\right)}\)
\(=\dfrac{x\left(x+2\right)-x^2}{2\left(x-2\right)\left(x+2\right)}\)
\(=\dfrac{x^2+2x-x^2}{2\left(x-2\right)\left(x+2\right)}\)
\(=\dfrac{2x}{2\left(x-2\right)\left(x+2\right)}\)
\(=\dfrac{x}{x^2-4}\)
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