Unclear. Did you mean
f(x)= [sqrt of x+3]
--------------------
(x+8)
or did you mean
3
f(x)= [sqrt of x] + ----------
x+8
I will focus on the first possibility. The domain of sqrt(x+3) is [-3,infinity).
The domain of x+3
------- is "x is not equal to -8."
x+8
Then the overall domain would be simply [-3, infinity).
