Answer
$x=-5$
Work Step by Step
Expressing the terms of the given equation, $
\dfrac{2}{x^2-4}=\dfrac{1}{x+2}-\dfrac{3}{x-2}
,$ in factored form results to
\begin{array}{l}\require{cancel}
\dfrac{2}{(x+2)(x-2)}=\dfrac{1}{x+2}-\dfrac{3}{x-2}
.\end{array}
Multiplying both sides by the $LCD=
(x+2)(x-2)
$, then the solution to the equation above is
\begin{array}{l}
1(2)=(x-2)(1)-(x+2)(3)
\\\\
2=x-2-3x-6
\\\\
-x+3x=-2-6-2
\\\\
2x=-10
\\\\
x=-\dfrac{10}{2}
\\\\
x=-5
.\end{array}
