Question

G(x) = (Use integers or fractions for any numbers in the expression)

Answer 1

`(f+g)(x) = (11x+9)/(9x-2)`

Explanation:

f(x) = (2x+9)/(9x-2)

g(x) = 9x/(9x-2)

Now,

(f + g)(x) will give,

`(f + g)(x) = (2x+9)/(9x-2) + 9x/(9x - 2)\\(f +g)(x) = ((2x+9)+9x)/(9x-2)\\(f+g)(x) = (2x+9x+9)/(9x-2)\\(f+g)(x) = (11x + 9)/(9x -2)`

Which is the answer

Answer 2

`(f+g)(x)=(11x+9)/(9x-2)`

Explanation:

Given functions:

`f(x)=(2x+9)/(9x-2)`

`g(x)=(9x)/(9x-2)`

To find (f + g)(x), simply add the two functions f(x) and g(x).

As both functions have the same denominator, we can apply the fraction rule:

`\boxed{ (a)/(c)+(b)/(c)=(a+b)/(c)}`

Therefore:

`\begin{aligned}(f+g)(x)&=f(x)+g(x)\\\\&=(2x+9)/(9x-2)+(9x)/(9x-2)\\\\&=(2x+9+9x)/(9x-2)\\\\&=(11x+9)/(9x-2)\end{aligned}`