Question

Give the domain of the variable in the following equation

Answer 1

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:

`\begin{gathered} 5x+9\\e0 \\ x\\e0 \\ 3x-4\\e0 \end{gathered}`

Solving each one of them, we get the following restrictions:

`x\\e-(9)/(5),\:0,\:(4)/(3)`

The domain is:

`\lbrace x|x\:is\:a\:real\:number,\quad x\\e-(9)/(5),0,\:(4)/(3)\rbrace`