\(=\dfrac{x+1}{6x^3}+\dfrac{2-x}{8x\left(x-1\right)\left(x+1\right)}\)
\(=\dfrac{4\left(x+1\right)^2\left(x-1\right)+3x^2\left(2-x\right)}{24x^3\left(x-1\right)\left(x+1\right)}\)
\(=\dfrac{4\left(x^2-1\right)\left(x+1\right)+6x^2-3x^3}{24x^3\left(x-1\right)\left(x+1\right)}\)
\(=\dfrac{4\left(x^3+x^2-x-1\right)+6x^2-3x^3}{24x^3\left(x-1\right)\left(x+1\right)}\)
\(=\dfrac{4x^3+4x^2-4x-4+6x^2-3x^3}{24x^3\left(x-1\right)\left(x+1\right)}\)
\(=\dfrac{x^3+10x^2-4x-4}{24x^3\left(x-1\right)\left(x+1\right)}\)
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