Answer
$x=\left\{ -1,\dfrac{3}{2} \right\}$
Work Step by Step
Multiplying both sides by the $LCD=
x^2
$, then the solution to the given equation, $
-\dfrac{3}{x^2}-\dfrac{1}{x}+2=0
,$ is
\begin{array}{l}
1(-3)-x(1)+x^2(2)=0
\\\\
-3-x+2x^2=0
\\\\
2x^2-x-3=0
\\\\
(2x-3)(x+1)=0
\\\\
x=\left\{ -1,\dfrac{3}{2} \right\}
.\end{array}
Upon checking, both solutions, $
x=\left\{ -1,\dfrac{3}{2} \right\}
,$ satisfy the original equation.