a: \(=\dfrac{2x^2}{x^2-1}+\dfrac{6}{x-3}-\dfrac{2x-6}{\left(x-3\right)\left(x^2-1\right)}\)
\(=\dfrac{2x^3-6x^2+6x^2-6-2x+6}{\left(x-3\right)\left(x^2-1\right)}\)
\(=\dfrac{2x\left(x-1\right)}{\left(x-3\right)\left(x-1\right)\left(x+1\right)}=\dfrac{2x}{\left(x-3\right)\left(x+1\right)}\)
b: \(=\dfrac{x+3}{x\left(x-6\right)}-\dfrac{x+9}{\left(x-6\right)\left(x+4\right)}+1\)
\(=\dfrac{\left(x+3\right)\left(x+4\right)-x\left(x+9\right)+x\left(x-6\right)\left(x+4\right)}{x\left(x-6\right)\left(x+4\right)}\)
\(=\dfrac{x^2+7x+12-x^2-9x+x\left(x^2-2x-24\right)}{x\left(x-6\right)\left(x+4\right)}\)
\(=\dfrac{-2x+12+x^3-2x^2-24x}{x\left(x-6\right)\left(x+4\right)}\)
\(=\dfrac{x^3-2x^2-26x+12}{x\left(x-6\right)\left(x+4\right)}\)
\(=\dfrac{x^3-6x^2+4x^2-24x-2x+12}{x\left(x-6\right)\left(x+4\right)}\)
\(=\dfrac{\left(x-6\right)\left(x^2+4x-2\right)}{x\left(x-6\right)\left(x+4\right)}=\dfrac{x^2+4x-2}{x^2+4x}\)