Solve the equation (3x−1)/(x−2)=0. What is the value of x?

A fraction is equal to zero only when its numerator is zero and its denominator is not zero.

Set the numerator equal to zero:

3x − 1 = 0
3x = 1
x = 1/3

Since x ≠ 2, the denominator is not zero, so x = 1/3 is the valid solution.

Why the other options are incorrect:

• 2: Makes the denominator zero, so the expression is undefined.
• -2: Does not make the numerator zero.
• 1/4: Does not satisfy the equation.