Question

find the domain of the rational expression: $\frac{x - 3}{2x - 8}$
all real numbers except 3
all real numbers except 8
all real numbers except 0
all real numbers except 4

Explanation:

Step1: Recall domain - finding rule

The domain of a rational expression $\frac{f(x)}{g(x)}$ is all real numbers except the values of $x$ that make the denominator $g(x)=0$.

Step2: Set the denominator equal to zero

For the rational expression $\frac{x - 3}{2x - 8}$, set the denominator $2x-8 = 0$.

Step3: Solve the equation for $x$

Add 8 to both sides of $2x - 8=0$: $2x=8$. Then divide both sides by 2, we get $x = 4$.

Answer:

all real numbers except 4