Answer
no solution
Work Step by Step
The factored form of the given equation, $
\dfrac{2}{x^2-4}=\dfrac{1}{2x-4}
,$ is
\begin{array}{l}\require{cancel}
\dfrac{2}{(x+2)(x-2)}=\dfrac{1}{2(x-2)}
.\end{array}
Multiplying both sides by the $LCD=
2(x+2)(x-2)
,$ then
\begin{array}{l}\require{cancel}
2(2)=(x+2)(1)
\\\\
4=x+2
\\\\
-x=2-4
\\\\
-x=-2
\\\\
x=2
.\end{array}
Upon checking, $x=2$ does not satisfy the original equation. Hence, there is $\text{
no solution
.}$
