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