a: \(=\dfrac{6x}{5\left(x-4\right)}-\dfrac{x}{\left(x-4\right)^2}\)
\(=\dfrac{6x^2-24x-5x}{5\left(x-4\right)^2}=\dfrac{6x^2-29x}{5\left(x-4\right)^2}\)
b: \(=\dfrac{4}{x+2}+\dfrac{3}{x-2}-\dfrac{5x+2}{\left(x-2\right)\left(x+2\right)}-\dfrac{x^2-2x+4}{x^3+8}\)
\(=\dfrac{4x-8+3x+6-5x-2}{\left(x+2\right)\left(x-2\right)}-\dfrac{1}{x+2}\)
\(=\dfrac{2x-2-x+2}{\left(x+2\right)\left(x-2\right)}\)
\(=\dfrac{x}{\left(x+2\right)\left(x-2\right)}\)
c: \(\left(\dfrac{x}{x-1}-\dfrac{x+1}{x}\right):\left(\dfrac{x}{x+1}-\dfrac{x-1}{x}\right)\)
\(=\dfrac{x^2-x^2+1}{x\left(x-1\right)}:\dfrac{x^2-x^2+1}{x\left(x+1\right)}\)
\(=\dfrac{x\left(x+1\right)}{x\left(x-1\right)}=\dfrac{x+1}{x-1}\)