\(\left(\dfrac{x}{3x-9}+\dfrac{2x-3}{3x-x^2}\right).\dfrac{3x^2-9x}{x^2-6x+9}\)
\(=\left[\dfrac{x}{3\left(x-3\right)}+\dfrac{2x-3}{x\left(3-x\right)}\right].\dfrac{3x\left(x-3\right)}{x^2-6x+9}\)
\(=\left[\dfrac{x}{3\left(x-3\right)}-\dfrac{2x-3}{x\left(x-3\right)}\right].\dfrac{3x\left(x-3\right)}{x^2-6x+9}\)
\(=\dfrac{x.x-3\left(2x-3\right)}{3x\left(x-3\right)}.\dfrac{3x\left(x-3\right)}{x^2-6x+9}\)
\(=\dfrac{x^2-6x+9}{3x\left(x-3\right)}.\dfrac{3x\left(x-3\right)}{x^2-6x+9}=1\)
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