for the given functions f and g find the following and state the domain of each result

Question

f(x)=3x+1/8x-9; g(x)=5x/8x-9
(they look like fractions)

A) (f+g)(x)=?
B)domain of (f+g)
c) (f/g)(x)=?
d) domain of f/g?

please show work

Answer 1

a. (f+g)x = (3x+1)/(8x-9) + 5x/(8x-9) =
(8x+1)/(8x-9).

b. 8x-9 = 0
8x = 9
X = 9/8.
When X = 9/8, the denominator becomes zero and the fraction undefined. Therefore, 9/8 is out of the domain.

Domain = All real values of X except 9/8: 9/8 > X > 9/8.

c. F(x)/G(x) = F(x) * 1/G(x).
F(x)/G(x) = (3x+1)/(8x-9) * (8x-9)/5x=
(3x+1)/5x.

d. The domain = all real values of X:

-Infinity < X < +Infinity.