For all $x \ne 3$, the expression $\dfrac{x^{2} - 9}{4x - 12}$ simplifies to:

Factor each part using two standard identities: - **Numerator** with $a^{2} - b^{2} = (a + b)(a - b)$: $x^{2} - 9 = (x + 3)(x - 3)$. - **Denominator** with $ca - cb = c(a - b)$: $4x - 12 = 4(x - 3)$. So $\dfrac{x^{2} - 9}{4x - 12} = \dfrac{(x + 3)(x - 3)}{4(x - 3)}$. The $(x - 3)$ factors cancel (valid since $x \ne 3$), leaving $\dfrac{x + 3}{4}$. Trap A is the sign mistake: forgetting that $x^{2} - 9$ factors with $(x + 3)$ in front, not $(x - 3)^{2}$. Trap D is what you get if you forget to cancel — technically equivalent for $x \ne 3$ but not simplified.