Answer
$x=-1$
Work Step by Step
The factored form of the given equation, $
\dfrac{x+3}{x^2+5x+6}=\dfrac{3}{2x+4}-\dfrac{1}{x+3}
,$ is
\begin{array}{l}\require{cancel}
\dfrac{x+3}{(x+3)(x+2)}=\dfrac{3}{2(x+2)}-\dfrac{1}{x+3}
.\end{array}
Multiplying both sides by the $LCD=
2(x+3)(x+2)
,$ the solution to the given equation is
\begin{array}{l}\require{cancel}
2(x+3)=(x+3)(3)-2(x+2)(1)
\\\\
2x+6=3x+9-2x-4
\\\\
2x-3x+2x=9-4-6
\\\\
x=-1
.\end{array}
