Step 1 :To find \((f+g)(x)\), we need to add the functions \(f(x)\) and \(g(x)\) together. This means we will add \(2+\frac{3}{x}\) and \(\frac{3}{x}\) together.
Step 2 :The domain of the function will be all real numbers except for \(x=0\), because we cannot divide by zero.
Step 3 :Let's calculate \((f+g)(x)\) and simplify the result.
Step 4 :\((f+g)(x)\) = 2 + \frac{6}{x}
Step 5 :\(\boxed{(f+g)(x)=2+\frac{6}{x}}\)
Step 6 :The domain of the function is all real numbers except for \(x=0\).