\(=\left(\dfrac{9}{x\left(x-3\right)\left(x+3\right)}+\dfrac{1}{x+3}\right):\left(\dfrac{x-3}{x\left(x+3\right)}-\dfrac{x}{3\left(x+3\right)}\right)\)
\(=\dfrac{9+x\left(x-3\right)}{x\left(x-3\right)\left(x+3\right)}:\dfrac{3x-9-x^2}{3x\left(x+3\right)}\)
\(=\dfrac{x^2-3x+9}{x\left(x-3\right)\left(x+3\right)}\cdot\dfrac{3x\left(x+3\right)}{-\left(x^2-3x+9\right)}\)
\(=\dfrac{-3}{x-3}\)
\(=\left(\dfrac{9}{x\left(x^2-9\right)}+\dfrac{1}{x+3}\right):\left(\dfrac{x-3}{x\left(x+3\right)}-\dfrac{x}{3\left(x+3\right)}\right)\)
\(=\left(\dfrac{9}{x\left(x-3\right)\left(x+3\right)}+\dfrac{1\cdot x\left(x-3\right)}{x\left(x-3\right)\left(x+3\right)}\right):\left(\dfrac{\left(x-3\right)\cdot3}{3x\left(x+3\right)}-\dfrac{x^2}{3x\left(x+3\right)}\right)\)
\(=\dfrac{9+x^2-3x}{x\left(x-3\right)\left(x+3\right)}:\dfrac{3x-9-x^2}{3x\left(x+3\right)}\)
\(=\dfrac{9+x^2-3x}{x\left(x-3\right)\left(x+3\right)}\cdot\dfrac{3x\left(x+3\right)}{3x-9-x^2}\)
\(=\dfrac{\left(9+x^2-3x\right)\cdot3x\left(x+3\right)}{x\left(x-3\right)\left(x+3\right)\cdot\left(3x-9-x^2\right)}\)
\(=\dfrac{\left(9+x^2-3x\right)\cdot3x\left(x+3\right)}{-x\left(x-3\right)\left(x+3\right)\cdot\left(-3x+9+x^2\right)}\)
\(=\dfrac{3x}{-x\left(x-3\right)}\)
\(=\dfrac{3}{-\left(x-3\right)}\)
\(=\dfrac{-3}{x-3}\)
