#### Answer

The equation has no solution.

#### Work Step by Step

$\dfrac{-2}{x-3}+\dfrac{3}{x+3}=\dfrac{-12}{x^{2}-9}$
Factor the denominator of the fraction on the right side of the equation:
$\dfrac{-2}{x-3}+\dfrac{3}{x+3}=\dfrac{-12}{(x-3)(x+3)}$
Multiply the whole equation by $(x-3)(x+3)$:
$(x-3)(x+3)\Big[\dfrac{-2}{x-3}+\dfrac{3}{x+3}=\dfrac{-12}{(x-3)(x+3)}\Big]$
$-2(x+3)+3(x-3)=-12$
Evaluate the indicated operations:
$-2x-6+3x-9=-12$
Take all terms without $x$ to the right side of the equation:
$-2x+3x=-12+6+9$
Simplify both sides:
$x=3$
The original equation is undefined for $x=3$, so the equation has no solution.