Find the value of x for which $\frac{x - 5}{x(x - 1)}$ is undefined.

Analyze the question: A fraction is undefined when its denominator equals zero, because division by zero has no meaning.

Concept: To find where a rational expression is undefined, set the denominator equal to zero and solve.

Solution:

The denominator is x(x − 1).

Set x(x − 1) = 0

Using the zero product rule, either:

• x = 0, or
• x − 1 = 0, which gives x = 1

So the expression is undefined when x = 0 or x = 1.

Check:

• If x = 0: the denominator is 0(0 − 1) = 0, so it is undefined.
• If x = 1: the denominator is 1(1 − 1) = 0, so it is undefined.

Note that x = 5 makes the numerator zero (5 − 5 = 0). That makes the whole fraction equal to 0, which is a perfectly valid value, not an undefined one. This is why option A is a trap.

Answer: The correct option is D (0 or 1).

Tip: "Undefined" always points to the denominator being zero. Ignore the numerator completely. Students often confuse this with finding the zeros of the expression, which come from the numerator.