Which expression is equivalent to (x²-4)/(x²+5x+6) for x ≠ -2, -3?

Factor both parts: $x^2-4=(x-2)(x+2)$ and $x^2+5x+6=(x+2)(x+3)$. Cancel the common factor $x+2$, which is allowed since $x\ne-2$: $\frac{x-2}{x+3}$, choice F. Check with $x=0$: the original is $\frac{-4}{6}=-\frac{2}{3}$ and $\frac{0-2}{0+3}=-\frac{2}{3}$. Choice G ($\frac{x+2}{x+3}$) cancels the wrong factor. Choice H ($\frac{x-2}{x-3}$) changes a sign in the denominator. Choice J ($x-2$) cancels the entire denominator as if it were one factor. Only common factors, never common terms, can be cancelled. The restrictions $x\ne-2,-3$ stay in force after cancelling.