Find the limit \( \lim \limits _{x \rightarrow 0} \frac{\frac{1}{x-1}+\frac{1}{x+1}}{x} \)

\( \lim_{x\rightarrow 0}\frac{\frac{1}{x-1}+\frac{1}{x+1}}{x} = \lim_{x\rightarrow 0}\frac{x+1+x-1}{(x+1)(x-1)(x)}=\lim_{x\rightarrow 0}\frac{2x}{(x+1)(x-1)(x)}=\lim_{x\rightarrow 0}\frac{2}{(x+1)(x-1)}=\frac{2}{(1)(-1)}=-2 \)