f(x)=x+2/x-5, g(x) = (6X-12)/(x^2 + 25) what is (f+g)(x)?

To find (f+g)(x), we need to add the functions f(x) and g(x) together.

Given:
f(x) = x+2/x-5
g(x) = (6x-12)/(x^2 + 25)

To add the two functions, we add the corresponding terms together.

(f+g)(x) = f(x) + g(x)

First, let's find the common denominator for the fractions in f(x) and g(x). The common denominator would be (x-5)(x^2 + 25).

f(x) = (x+2)/(x-5) * (x^2 + 25)/(x^2 + 25)
= (x^3 + 25x + 2x + 50)/(x^3 - 5x^2 + 25x - 125)
= (x^3 + 27x + 50)/(x^3 - 5x^2 + 25x - 125)

g(x) = (6x-12)/(x^2 + 25)

Now, we can add the two functions together:

(f+g)(x) = f(x) + g(x)
= (x^3 + 27x + 50)/(x^3 - 5x^2 + 25x - 125) + (6x-12)/(x^2 + 25)

However, further simplification is not possible without additional instructions or values for x.