Answer
$\{x\in \mathbb{R}|x\neq-2$ and $x\displaystyle \neq\frac{8}{5}\}$
Work Step by Step
The domain of the combined function $(f/g)(x)=\displaystyle \frac{f(x)}{g(x)}$
is the intersection of domains of f and g, with the additional condition:$ g(x)\neq 0.$
The domain of f is $\{x\in \mathbb{R}|x\neq-2\}$ (see previous exercise).
The domain of g is $\mathbb{R}$.
We exclude the x-values for which $g(x)=0,$
$5x-8=0$
$5x=8$
$x=\displaystyle \frac{8}{5}$
Domain of $f/g$ is $\{x\in \mathbb{R}|x\neq-2$ and $x\displaystyle \neq\frac{8}{5}\}$
