Answer
$x=\{-7,7\}$
Work Step by Step
Multiplying both sides by the $LCD=
7x
$, the value of the variable that satisfies the given equation, $
\dfrac{7}{x}-\dfrac{x}{7}=0
,$ is
\begin{array}{l}\require{cancel}
7(7)-x(x)=7x(0)
\\\\
49-x^2=0
\\\\
(7+x)(7-x)=0
\\\\
x=\{-7,7\}
.\end{array}