Answer
$2x$
Work Step by Step
The given expression, $
\dfrac{(x+2)^{-1}+(x-2)^{-1}}{(x^2-4)^{-1}}
,$ simplifies to
\begin{array}{l}\require{cancel}
\dfrac{\dfrac{1}{x+2}+\dfrac{1}{x-2}}{\dfrac{1}{x^2-4}}
\\\\=
\dfrac{\dfrac{(x-2)(1)+(x+2)(1)}{(x+2)(x-2)}}{\dfrac{1}{(x+2)(x-2)}}
\\\\=
\dfrac{\dfrac{(x-2)(1)+(x+2)(1)}{\cancel{(x+2)(x-2)}}}{\dfrac{1}{\cancel{(x+2)(x-2)}}}
\\\\=
\dfrac{(x-2)(1)+(x+2)(1)}{1}
\\\\=
(x-2)(1)+(x+2)(1)
\\\\=
x-2+x+2
\\\\=
2x
.\end{array}
