Answer
$x=-8$
Work Step by Step
$\dfrac{3}{x+3}=\dfrac{5}{2x+6}+\dfrac{1}{x-2}$
Take out common factor $2$ from the denominator of the first fraction on the right side:
$\dfrac{3}{x+3}=\dfrac{5}{2(x+3)}+\dfrac{1}{x-2}$
Multiply the whole equation by $2(x+3)(x-2)$:
$2(x+3)(x-2)\Big[\dfrac{3}{x+3}=\dfrac{5}{2(x+3)}+\dfrac{1}{x-2}\Big]$
$(2)(x-2)(3)=(5)(x-2)+(2)(x+3)$
$6x-12=5x-10+2x+6$
Take all terms with $x$ to the left side and all terms without $x$ to the right side and solve for $x$:
$6x-5x-2x=-10+6+12$
$-x=8$
$x=-8$
