Factoring

Let’s stay with the limit you brought in: (x² − 4) / (x − 2) as x approaches 2. You noticed direct substitution gives 0/0. That is an important signal, but it is not yet a conclusion. What does x² − 4 factor into?

Yes—the factorization is right, and it exposes why substitution looked broken. For every x near 2 except x = 2, the shared (x − 2) can be removed. After that cancellation, what value does the remaining expression approach?