Find the domain:
a) [sqrt(x+3)]+[5x^2-180]
b) [sqrt(x+3)]/[5x^2-180]
c) (8x+9)(9x+8)
d) (8x+9)/(9x+8)
e) [sqrt(x+2)](5x^2-245)
f) [sqrt(x+2)]/(5x^2-245)
all polynomials have domain of (-∞,+∞)
√u has domain u >= 0
rational functions have domains which exclude where the denominator is zero.
Keeping that in mind, I'll do (b), and the rest should be easy.
√(x+3) needs x+3 >= 0, or x >= -3
the domain also excludes x=±6, since then 5x^2-180=0, and you cannot divide by zero. -6 is already excluded by the √, so the domain is [-3,6)∪(6,∞)