Question

Someone help me please and thank you!! ASAP :(

Answer 1

Answer: Choice D)

Work Shown:

`(f+g)(x) = f(x)+g(x)\\\\(f+g)(x) = (x-23)/(x^2+9x-36)+(1)/(x+12)\\\\(f+g)(x) = (x-23)/((x+12)(x-3))+(1(x-3))/((x+12)(x-3))\\\\(f+g)(x) = (x-23+1(x-3))/((x+12)(x-3))\\\\(f+g)(x) = (x-23+x-3)/(x^2+9x-36)\\\\(f+g)(x) = (2x-26)/(x^2+9x-36)\\\\`

We must require that
`x \\e -12` and
`x \\e 3` to avoid having 0 in the denominator. This is why choice D is the answer.