Which of these values would make $\frac{3p - 1}{p^{2} - p}$ undefined?

Analyze the question: A fraction is undefined when its denominator equals zero. So we need the values of p that make p² − p = 0.

Concept: Division by zero is not allowed. To find where a rational expression is undefined, set the denominator equal to 0 and solve.

Solution:

Set the denominator to zero:

p² − p = 0

Factorise:

p(p − 1) = 0

So p = 0 or p = 1.

The expression is undefined at p = 0 and p = 1.

Check the options:

• A. p = 1 → denominator = 1 − 1 = 0, so the expression is undefined. ✔
• B. p = 1/3 → denominator = 1/9 − 1/3 = −2/9, which is defined.
• C. p = −1/3 → denominator = 1/9 + 1/3 = 4/9, which is defined.
• D. p = −1 → denominator = 1 + 1 = 2, which is defined.

Only option A makes the denominator zero.

Tip: For "undefined" questions, ignore the numerator and look only at the denominator. Factorise it and find the values that make it zero. Be careful not to confuse this with the values that make the numerator zero (here p = 1/3, which would make the expression equal to 0, not undefined).