Answer
Check work for reasoning.
Work Step by Step
$f+g$ is continuous for all values of x.
$\dfrac{f}{g}$ is not necessarily continuous for all values of $x$ since $g$ could be zero.
Example to prove why the quotient is not necessarily continuous:
Both $(x-4)$ and $(x-2)$ are continuous for all values of $x$ but $\dfrac{(x-4)}{(x-2)}$ has a discontinuity (vertical asymptote) at $x=2$ and hence it is not continuous for all values of $x.$
