\(\dfrac{5x}{x-3}+\dfrac{x}{x+3}-\dfrac{6x}{9-x^2}\left(x\ne\pm3\right)\)
\(\Leftrightarrow\dfrac{5x\left(x+3\right)+x\left(x-3\right)+6x}{x^2-9}\)
\(\Leftrightarrow\dfrac{5x^2+15x+x^2-3x+6x}{x^2-9}\)
\(\Leftrightarrow\dfrac{6x^2+18x}{x^2-9}\Leftrightarrow\dfrac{6\left(x^2+9\right)}{x^2-9}\)