Answer
$\dfrac{-6x}{(x+3)(x-3)(x-3)}$
Work Step by Step
The given expression, $
\dfrac{3}{x^2-9}-\dfrac{x}{x^2-6x+9}+\dfrac{1}{x+3}
,$ simplifies to
\begin{array}{l}\require{cancel}
\dfrac{3}{(x+3)(x-3)}-\dfrac{x}{(x-3)(x-3)}+\dfrac{1}{x+3}
\\\\
\dfrac{(x-3)(3)-(x+3)(x)+(x-3)(x-3)(1)}{(x+3)(x-3)(x-3)}
\\\\
\dfrac{3x-9-x^2-3x+x^2-6x+9}{(x+3)(x-3)(x-3)}
\\\\
\dfrac{(-x^2+x^2)+(3x-3x-6x)+(-9+9)}{(x+3)(x-3)(x-3)}
\\\\
\dfrac{-6x}{(x+3)(x-3)(x-3)}
.\end{array}
