Answer
$(-\infty,4)\; or \; (4,+\infty)$.
Work Step by Step
The given functions are
$f(x)=\frac{9x}{x-4}$ and $g(x)=\frac{7}{4-x}$
$\Rightarrow f(x)+g(x)=\frac{9x}{x-4}+\frac{7}{4-x}$
Multiply and divide the second fraction:
$\Rightarrow f(x)+g(x)=\frac{9x}{x-4}+\frac{-7}{-(4-x)}$
$\Rightarrow f(x)+g(x)=\frac{9x}{x-4}-\frac{7}{(x-4)}$
Add both numerators because both denominators are equal.
$\Rightarrow f(x)+g(x)=\frac{9x-7}{(x-4)}$
In the denominator the value of $x$ must not be $4$.
Hence, the domain is $(-\infty,4)\; or \; (4,+\infty)$.
