Answer
$x=-2$
Work Step by Step
Multiplying both sides by the $LCD=
3x
,$ then the solution to the given equation, $
\dfrac{3}{x}-\dfrac{x+21}{3x}=\dfrac{5}{3}
,$ is
\begin{array}{l}\require{cancel}
3(3)-1(x+21)=x(5)
\\\\
9-x-21=5x
\\\\
-x-5x=-9+21
\\\\
-6x=12
\\\\
x=\dfrac{12}{-6}
\\\\
x=-2
.\end{array}
