Question

Find the domain of the rational expression: x-4/2x-6

1. all real numbers except 3
2. all real numbers except 6
3. all real numbers except O
4. all real numbers except 4

Answer 1

All real numbers except 3

Explanation:

Given

`(x - 4)/(2x - 6)`

Required

Determine the domain

We start by writing the following inequality

`2x - 6 \\eq 0`

Add 6 to both sides

`2x -6 + 6 \\eq = 0 + 6`

`2x \\eq 6`

Divide both sides by 2

`(2x)/(2)\\eq (6)/(2)`

`x \\eq (6)/(2)`

`x \\eq = 3`

As such, the domain of x is all real numbers except 3