DTFT Pairs confusion
I would really recommend that you compute the DTFT of the sequences $x_1[n]=a^nu[n]$ and $x_2[n]=-a^nu[-n-1]$. This is very straightforward if you use the formula for the geometric series:
$$\sum_{n=0}^{\infty}q^n=\frac{1}{1-q},\qquad |q|&lt;1\tag{1}$$
It will be important to consider the magnitude of $a$. Note that it's not for nothing that the table in your question specifies a condition on $|a|$.