Answer
$[3, \infty)$
Work Step by Step
Here, $f(x)=\sqrt{x-3}$ and $g(x)=\sqrt{x+1}$
In order to find the domain we will have to set the equation inside the square root greater than and equal to zero.
we have, $x-3 \geq 0$ and $x+1 \geq 0$
or, $x \geq 3$ and $x \geq -1$
Thus, Domain for $f(x)+g(x)$ and $\dfrac{f(x)}{g(x)}$ will be a set of interval to both domains, that is, $[3, \infty)$
