#### Answer

$-\frac{6}{5}$, $\frac{6}{5}$

#### Work Step by Step

The additive inverse of a number $a$ is $-a$. Therefore, the additive inverse of $\frac{6}{5}$ is $-(\frac{6}{5})=-\frac{6}{5}$.
The absolute value of a number $a$ is equal to $a$ if $a\geq0$ and is equal to $-a$ if $a\lt0$. Therefore, $|\frac{6}{5}|=\frac{6}{5}$.