a: \(=\dfrac{2}{x-3}+\dfrac{2x}{\left(x-3\right)\left(x-1\right)}+\dfrac{x}{x-1}\)
\(=\dfrac{2x-2+2x+x^2-3x}{\left(x-3\right)\left(x-1\right)}=\dfrac{x^2+x-2}{\left(x-3\right)\left(x-1\right)}=\dfrac{x+2}{x-3}\)
b: \(=\dfrac{x^2-2x+2x+4+4x}{\left(x-2\right)\left(x+2\right)}=\dfrac{\left(x+2\right)^2}{\left(x-2\right)\left(x+2\right)}=\dfrac{x+2}{x-2}\)
c: \(=\dfrac{-x-1}{x-3}+\dfrac{2x-1}{x+3}-\dfrac{x\left(x-1\right)}{\left(x-3\right)\left(x+3\right)}\)
\(=\dfrac{-x^2-4x-3+2x^2-6x-x-3-x^2+x}{\left(x-3\right)\left(x+3\right)}\)
\(=\dfrac{-10x-6}{\left(x-3\right)\left(x+3\right)}\)
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