Question

what is the domain of $f(x)=\frac{3x}{x - 1}$?
all real numbers
all nonzero numbers
all real numbers except 1
all real numbers except 3

Explanation:

Step1: Identify undefined condition

A rational function is undefined when its denominator equals 0. Set the denominator equal to 0:
$x-1=0$

Step2: Solve for excluded x-value

Solve the equation from Step1:
$x=1$

Step3: Define the domain

The function is defined for all real numbers except the value that makes the denominator 0.

Answer:

all real numbers except 1