The domain of the function $\frac{{10}^x+{10}^{-x}}{{10}^x-{10}^{-x}}$ is 

The given function is $f\left(x\right)=\frac{{10}^x+{10}^{-x}}{{10}^x-{10}^{-x}}$

The above function is defined when the denominator is not equal to zero

Suppose that 

    $\begin{array}{rcl}{10}^x-{10}^{-x}& =& 0\\ {10}^x& =& {10}^{-x}\\ 2x& =& 0\\ x& =& 0\end{array}$

Therefore, the domain of the function $f\left(x\right)=\frac{{10}^x+{10}^{-x}}{{10}^x-{10}^{-x}}$ is $\boxed{R-\left\{0\right\}}$