For what value of x is $\frac{4 - 2x}{x + 1}$ undefined.

Analyze the question

A fraction is undefined when its denominator equals zero, because division by zero has no meaning. So we need the value of x that makes the denominator x + 1 equal to zero.

Explain the concept

For a rational expression like P(x)/Q(x), the expression is undefined whenever Q(x) = 0. The numerator does not matter here. It only decides when the fraction equals zero, not when it is undefined.

Solution

Set the denominator equal to zero:

x + 1 = 0

x = -1

Check: Substitute x = -1 into the expression:

(4 - 2(-1)) / (-1 + 1) = 6 / 0, which is undefined. ✓

Checking the other options:

• x = 2 gives (4 - 4)/3 = 0, which is defined (it equals 0).
• x = 1 gives 2/2 = 1, which is defined.
• x = -2 gives 8/(-1) = -8, which is defined.

Answer: The correct option is B (-1).

Exam tip: When you see "undefined" in a fraction question, ignore the numerator and set the denominator to zero. Don't confuse A (x = 2) with the answer. That value makes the numerator zero, so the fraction equals 0 and is perfectly defined.