Chapter 6 - Section 6.5 - Solving Equations Containing Rational Expressions - Exercise Set - Page 378: 42

$x=-1$

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}