Question

find the domain of the rational expression: \\(\frac{x - 3}{2x - 8}\\)
options:

• all real numbers except 3
• all real numbers except 8
• all real numbers except 0
• all real numbers except 4

Explanation:

Step1: Identify the denominator

The rational expression is $\frac{x - 3}{2x - 8}$. The denominator cannot be zero.

Step2: Set denominator equal to zero

Set $2x - 8 = 0$.

Step3: Solve for x

Add 8 to both sides: $2x = 8$. Divide by 2: $x = 4$. So the domain is all real numbers except 4.

Answer:

all real numbers except 4 (corresponding to the option "all real numbers except 4")