Answer
$x=2$
Work Step by Step
Multiplying both sides by the $LCD=
30
$, the given expression, $
\dfrac{x-2}{5}+\dfrac{x+2}{2}=\dfrac{x+4}{3}
,$ is equivalent to
\begin{array}{l}\require{cancel}
6(x-2)+15(x+2)=10(x+4)
\\\\
6x-12+15x+30=10x+40
\\\\
6x+15x-10x=40+12-30
\\\\
11x=22
\\\\
x=\dfrac{22}{11}
\\\\
x=2
.\end{array}