if f(x) = x+1/x^2-9 and g(x) = x/x-3, find

Question

a) the domain of f(x)
b) the domain of g(x)
c) (f+g) (x)
d) the domain of (f+g) (x)

Answer 1

assuming that you meant:
f(x) = (x+1)/(x^2-9) and g(x) = x/(x-3)

The domain for both f(x) and g(x) are all values of x except those that make the denominator zero
domain of f(x): all x's except x = ±3
domain of g(x): all x/s except x = 3

(f+g)(x) = (x+1)/(x^2 - 9) + x/(x-3)
the LCD is x^2 - 9 or (x+3)(x-3)
= (x+1 + x(x+3))/(x^2 - 9)
= (x^2 + 4x + 1)/(x^2 - 9(

the domain of that is the same as the domain of f(x)