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. 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