a: \(=\left(\dfrac{1}{x\left(x+1\right)}+\dfrac{x+2}{x+1}\right):\dfrac{x^2-2x+1}{x}\)
\(=\dfrac{1+x^2+2x}{x\left(x+1\right)}\cdot\dfrac{x}{\left(x-1\right)^2}=\dfrac{x+1}{\left(x-1\right)^2}\)
b: \(=\left(\dfrac{-3x}{3x-1}+\dfrac{2x}{3x+1}\right)\cdot\dfrac{\left(3x-1\right)^2}{2x\left(3x+5\right)}\)
\(=\dfrac{-9x^2-3x+6x^2-2x}{\left(3x-1\right)\left(3x+1\right)}\cdot\dfrac{\left(3x-1\right)^2}{2x\left(3x+5\right)}\)
\(=\dfrac{-x\left(3x+5\right)}{\left(3x+1\right)}\cdot\dfrac{3x-1}{2x\left(3x+5\right)}=\dfrac{-3x+1}{2}\)
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