Simplify: (x² − 9) / (x − 3), assuming x ≠ 3

Factor and cancel. Numerator: x² − 9 = (x + 3)(x − 3) (difference of squares). Denominator: x − 3. Rewrite: [(x + 3)(x − 3)] / (x − 3). Cancel the (x − 3) factor: x + 3. The simplification is valid for x ≠ 3 (because at x = 3, the original expression has 0/0, undefined). For all other values of x, (x² − 9)/(x − 3) = x + 3. Strategy for simplifying rational expressions: (1) Factor numerator and denominator completely; (2) Cancel common factors; (3) State any restrictions on the variable (values that would make the original denominator zero). Common simplifications: (1) (x² − 4)/(x + 2) = (x + 2)(x − 2)/(x + 2) = x − 2; (2) (x² + 5x + 6)/(x + 2) = (x + 2)(x + 3)/(x + 2) = x + 3; (3) (x² − 25)/(x² + 10x + 25) = (x − 5)(x + 5)/(x + 5)² = (x − 5)/(x + 5). Don't cancel terms inside a sum — only factors of products. (x + 3)/(x + 5) does NOT simplify to 3/5 — those are terms, not factors.