Answer
$x=\dfrac{2}{7}$
Work Step by Step
The factored form of the given equation, $ \dfrac{3}{x+2}-\dfrac{1}{5x}=\dfrac{2}{5x^2+10x} ,$ is \begin{array}{l}\require{cancel} \dfrac{3}{x+2}-\dfrac{1}{5x}=\dfrac{2}{5x(x+2)} .\end{array} Multiplying both sides by the $LCD= 5x(x+2) ,$ then the given equation simplifies to \begin{array}{l}\require{cancel} 5x(3)-(x+2)(1)=1(2) \\\\ 15x-x-2=2 \\\\ 15x-x=2+2 \\\\
14x=4
\\\\
x=\dfrac{4}{14}
\\\\
x=\dfrac{\cancel{2}\cdot2}{\cancel{2}\cdot7}
\\\\
x=\dfrac{2}{7}
.\end{array}
