The domain is the set of possible inputs for our expression. The restrictions on the domain are the inputs that results in an indetermination on the expression. The denominator of a fraction cannot be zero, therefore, we have the following restrictions for our equation:
[tex]\begin{gathered} 5x+9\ne0 \\ x\ne0 \\ 3x-4\ne0 \end{gathered}[/tex]
Solving each one of them, we get the following restrictions:
[tex]x\ne-\frac{9}{5},\:0,\:\frac{4}{3}[/tex]
The domain is:
[tex]\lbrace x|x\:is\:a\:real\:number,\quad x\ne-\frac{9}{5},0,\:\frac{4}{3}\rbrace[/tex]
