Find the domain of $ \large e^{\ln\frac{x}{x+8}} $
My solution:
Set $f(x) = \large e^{\ln\frac{x}{x+8}}$, Now, we know $ e^{\ln x} = x$. So,$f(x) = \frac{x}{x+8}$
But again for the domain, since the $\ln $ cannot take negative values we have to assume that $\frac{x}{x+8} \gt 0$, which gives $ \frac{x}{x+8} \gt 0 \implies x<-8 \text{ or } x\gt 0$
but, according to someone I know it's actually, $\frac{x}{x+8}\neq 0 $.
But that mean we are operating the $e$ function first and then the rest, but why shouldn't we take care of the $\ln $ first? where exactly I am going wrong?