Find the value of x for which the expression (x² - 4x + 4) / (x - 2) is undefined.

## **The reasoning** A fraction is **undefined** when its denominator equals zero — because you can't divide by zero in mathematics. Here, the denominator is **(x - 2)**. Set it equal to zero: x - 2 = 0 x = 2 So when **x = 2**, the expression becomes (something)/**0**, which is undefined. Notice the numerator x² - 4x + 4 = (x - 2)² also equals zero when x = 2, giving us **0/0** — still undefined! The concept: *look at the denominator alone* to find where division breaks down. --- ## **Why the wrong options tempt you** **A) 0** — Students might think "zero makes things undefined," but substitute: (0 - 0 + 4)/(0 - 2) = 4/(-2) = -2. Perfectly defined! **C) -2** — Looks similar to 2, but check: (4 + 8 + 4)/(-2 - 2) = 16/(-4) = -4. Still defined. **D) 4** — Might come from solving the numerator, but (16 - 16 + 4)/(4 - 2) = 4/2 = 2. Also defined. --- ## **Quick takeaway** **A fraction dies when the bottom line hits zero** — always set the denominator to zero to find undefined values.