For the given functions $f$ and g, complete parts (a)-(h). For parts (a)-(d), also find the domain.
\[
f(x)=2+\frac{3}{x} ; g(x)=\frac{3}{x}
\]
(a) Find $(f+g)(x)$.
\[
(f+g)(x)=\square(\text { Simplify your answer. })
\]
Answer
The domain of the function is all real numbers except for \(x=0\).
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 \(x=0\).
