#### Answer

The equation has no solution.

#### Work Step by Step

$\dfrac{5}{x+2}+\dfrac{3}{x-2}=\dfrac{12}{(x+2)(x-2)}$
Multiply the whole equation by $(x+2)(x-2)$:
$(x+2)(x-2)\Big[\dfrac{5}{x+2}+\dfrac{3}{x-2}=\dfrac{12}{(x+2)(x-2)}\Big]$
$5(x-2)+3(x+2)=12$
$5x-10+3x+6=12$
Take all terms without $x$ to the right side of the equation and solve for $x$:
$5x+3x=12+10-6$
$8x=16$
$x=\dfrac{16}{8}$
$x=2$
Since the original equation is undefined for $x=2$, it has no solution.