#### Answer

The equation has no solution.

#### Work Step by Step

$\dfrac{-x}{x+1}-\dfrac{1}{x-1}=\dfrac{-2}{x^{2}-1}$
Factor the denominator of the fraction on the right side of the equation:
$\dfrac{-x}{x+1}-\dfrac{1}{x-1}=\dfrac{-2}{(x-1)(x+1)}$
Multiply the whole equation by $(x-1)(x+1)$:
$(x-1)(x+1)\Big[\dfrac{-x}{x+1}-\dfrac{1}{x-1}=\dfrac{-2}{(x-1)(x+1)}\Big]$
$-x(x-1)-(x+1)=-2$
Evaluate the indicated operations:
$-x^{2}+x-x-1=-2$
Take $2$ to the left side and simplify:
$-x^{2}+x-x-1+2=0$
$-x^{2}+1=0$
Rearrange:
$x^{2}-1=0$
Solve by factoring:
$(x-1)(x+1)=0$
Set both factors equal to $0$ and solve each individual equation for $x$:
$x-1=0$
$x=1$
$x+1=0$
$x=-1$
The original equation is undefined for $x=1$ and $x=-1$, so it has no solution.