Simplify $\frac{x^2-5x+6}{x^2-4}\cdot \frac{x+2}{x-3}$ and state any excluded $x$-values.

$1$, with no exclusions

$1$, with $x\ne 2$, $x\ne -2$, $x\ne 3$

$\frac{x-3}{x+2}$ with $x\ne 2$

$\frac{x+2}{x-3}$ with $x\ne \pm 2$, $x\ne 3$ since multiplication is distributive and cancellation is only partial