Answer
$ y $ is continuous in the domain
$ R-\{5,-2\}$
Work Step by Step
Given $$ y=\frac{x+3}{x^2-3x-10}$$
Find the zeros of the denominator
$ x^2-3x-10=0 \Rightarrow (x-5)(x+2)=0\\$
$ \Rightarrow (x-5)=0 \Rightarrow x=5$
$ \Rightarrow (x+2)=0\Rightarrow x=-2$
So, $ y $ is continuous in the domain
$ R-\{5,-2\}$
(All values except 5 and -2).
