f/g can be determined as,
[tex]\begin{gathered} \frac{f}{g}=\frac{\frac{9}{x+5}}{\frac{4}{x}} \\ =\frac{9x}{4(x+5)} \end{gathered}[/tex]
Domain of f(x) is,
[tex]\begin{gathered} x+5\ne0 \\ x\ne-5 \end{gathered}[/tex]
Domain of g(x) is,
[tex]x\ne0[/tex]
Thus, the domain of f/g is,
[tex]\begin{gathered} x\ne0\text{ and x}\ne-5 \\ x\in R-\lbrace-5,0\rbrace \end{gathered}[/tex]
Thus, above expression gives the required domain of f/g.
