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