Domain of exponential function

Question

I have $$e^{\frac{x²+2}{x-1}}.$$ As the domain is the values for which the function is defined, I thought of making the denominator of the power equal to zero. So $x-1=0$ and the function is undefined at $x=1$. Thus the domain goes from $-\infty$ to $1$ and 1 to $\infty$. Am I correct?

Answer 1

Yes, you would write the domain as $x\ne 1, x\in\Bbb R$ (unless you're including complex numbers, but thats a different kettle of fish)