Never factor again — graph both and look

(x² − 4)/(x² + x − 6) · (x² + 5x + 6)/(x² − x − 2), for x ≠ −3, −1, 2

Which expression is equivalent? (A) (x + 2)²/((x − 2)(x + 1)) (B) (x − 2)²/((x + 2)(x + 1)) (C) (x + 2)/(x + 1) (D) (x + 2)(x + 3)/((x − 2)(x + 1))

Equivalent means the same graph. Type the expression into Desmos as y = exactly as it is printed, then type the answer choices one at a time. A wrong choice draws a different curve; the equivalent one lands exactly on top of the original. Overlap on screen is strong evidence, not proof, so evaluate both at one or two x-values (not −3, −1 or 2) to confirm they match. On paper this is factoring all four quadratics, cancelling in exactly the right places and rebuilding what is left, and one bad factor ruins it.

Answer: (x + 2)²/((x − 2)(x + 1)) — answer A