\(\dfrac{x+3}{x-3}-\dfrac{x-3}{x+3}=\dfrac{9}{x^2-9}\left(ĐKXĐ:x\ne\pm3\right)\)
\(\Leftrightarrow\dfrac{\left(x+3\right)^2-\left(x-3\right)^2}{\left(x-3\right)\left(x+3\right)}=\dfrac{9}{\left(x-3\right)\left(x+3\right)}\)
\(\Rightarrow x^2+6x+9-x^2+6x-9=9\)
\(\Leftrightarrow12x=9\)
\(\Leftrightarrow x=\dfrac{3}{4}\) (nhận).
Vậy \(S=\left\{\dfrac{3}{4}\right\}\)