Compute z-transform of x[n]
$ x[n] = 3^n u[-n-1] $
We can easily determine that the signal is left sided by the $ u[-n-1] $ term.
$ X(z) = \sum_{n=-\infty}^{\infty}x[n]z^{-n} $
$ X(z) = \sum_{n=-\infty}^{\infty}3^n u[-n-1]z^{-n} $
Let $ k=-n-1 $
$ X(z) = \sum_{k=-\infty}^{\infty}3^{-k-1} u[k]z^{k+1} $
$ X(z) = \sum_{k=0}^{\infty}3^{-k-1}z^{k+1} $
$ X(z) = \frac{z}{3} \sum_{k=0}^{\infty}(\frac{z}{3})^k $
$ X(z) = \frac{z}{3}(\frac{1}{1-\frac{z}{3}}) $
Only if $ |\frac{z}{3}| < 1 $
$ X(z) = \frac{z}{3-z} $
Region of Convergence: $ |z| < 3 $
