#### Answer

$x=-1$

#### Work Step by Step

Multiplying both sides by the $LCD= x(x+3) ,$ then the solution to the given equation, $ 2+\dfrac{3}{x}=\dfrac{2x}{x+3} ,$ is \begin{array}{l}\require{cancel} x(x+3)(2)+(x+3)(3)=x(2x)
\\\\
2x^2+6x+3x+9=2x^2
\\\\
(2x^2-2x^2)+(6x+3x)=-9
\\\\
9x=-9
\\\\
x=-\dfrac{9}{9}
\\\\
x=-1
.\end{array}