Answer
$x=\left\{\dfrac{3}{2}, 5 \right\}$
Work Step by Step
Multiplying both sides by the $LCD=
x^2
$, the value of the variable that satisfies the given equation, $
2+\dfrac{15}{x^2}=\dfrac{13}{x}
,$ is
\begin{array}{l}\require{cancel}
x^2(2)+1(15)=x(13)
\\\\
2x^2+15=13x
\\\\
2x^2-13x+15=0
\\\\
(2x-3)(x-5)=0
\\\\
x=\left\{\dfrac{3}{2}, 5 \right\}
.\end{array}
