Answer
$\frac{-x^2-1}{(x^2-1)^2}$
Work Step by Step
Using the quotient rule: ($\frac{f}{g}$)^1: $\frac{g*f^1-g^1*f}{g^2}$
f(x)=$\frac{x}{x^{2}-1}$
f=x
$f^1$=1
g=$x^2-1$
$g^1$=2x
Now plug numbers into the quotinet rule formula: $\frac{(x^2-1)(1)-(2x)(x)}{(x^2-1)^2}$
simplify.... $\frac{x^2-1-2x^2}{(x^2-1)^2}$
simplify more... $\frac{-x^2-1}{(x^2-1)^2}$