Simplify: (3x² - 12) / (x - 2)

## The reasoning This is about **factoring before simplifying rational expressions**. First, look at the numerator: 3x² - 12. Notice both terms share a common factor of 3: 3x² - 12 = 3(x² - 4) Now, x² - 4 is a **difference of two squares** (a² - b² = (a+b)(a-b)), so: x² - 4 = (x + 2)(x - 2) Therefore: 3x² - 12 = 3(x + 2)(x - 2) Now substitute back: (3x² - 12)/(x - 2) = [3(x + 2)(x - 2)]/(x - 2) Cancel the common factor (x - 2): = 3(x + 2) ✓ ## Why the wrong options tempt you **B) 3(x - 2)** — You might cancel incorrectly and keep the wrong factor. **C) x + 2** — You forgot to carry the 3 from the factoring step. **D) 3x + 6** — This *equals* 3(x + 2), but the question asks you to simplify, and factored form is simpler. ## Quick takeaway Always factor completely *before* canceling—look for common factors first, then special patterns like difference of squares!