#### Answer

The equation has no solution.

#### Work Step by Step

$\dfrac{3}{x-2}+\dfrac{1}{x+2}=\dfrac{12}{x^{2}-4}$
Factor the denominator of the fraction on the right side of the equation:
$\dfrac{3}{x-2}+\dfrac{1}{x+2}=\dfrac{12}{(x-2)(x+2)}$
Multiply the whole equation by $(x-2)(x+2)$:
$(x-2)(x+2)\Big[\dfrac{3}{x-2}+\dfrac{1}{x+2}=\dfrac{12}{(x-2)(x+2)}\Big]$
$3(x+2)+x-2=12$
Evaluate the indicated operations:
$3x+6+x-2=12$
Take all terms without $x$ to the right side of the equation:
$3x+x=12-6+2$
Simplify both sides:
$4x=8$
Solve for $x$:
$x=\dfrac{8}{4}$
$x=2$
The original equation is undefined for $x=2$, so the equation has no solution.