\(=\dfrac{x+4}{x\left(x-4\right)}+\dfrac{4}{x\left(x+4\right)}+\dfrac{x+20}{\left(x-4\right)\left(x+4\right)}\)
\(=\dfrac{x^2+8x+16+4x-16+x^2+20x}{x\left(x+4\right)\left(x-4\right)}\)
\(=\dfrac{2x^2+32x}{x\left(x+4\right)\left(x-4\right)}=\dfrac{2x\left(x+16\right)}{x\left(x+4\right)\left(x-4\right)}=\dfrac{2\left(x+16\right)}{\left(x+4\right)\left(x-4\right)}\)
\(=\dfrac{x+4}{x\left(x-4\right)}+\dfrac{4}{x\left(x+4\right)}+\dfrac{x-20}{\left(x-4\right)\left(x+4\right)}\)
\(=\dfrac{\left(x+4\right)\left(x+4\right)}{x\left(x-4\right)\left(x+4\right)}+\dfrac{4\left(x-4\right)}{x\left(x-4\right)\left(x+4\right)}+\dfrac{x\left(x-20\right)}{x\left(x-4\right)\left(x+4\right)}\)
\(=\dfrac{x^2+8x+16+4x-16+x^2-20x}{x\left(x-4\right)\left(x+4\right)}\)
\(=\dfrac{2x^2-8x}{x\left(x-4\right)\left(x+4\right)}\)
\(=\dfrac{2x\left(x-4\right)}{x\left(x-4\right)\left(x+4\right)}\)
\(=\dfrac{2}{x+4}\)
