Simplifications
Simplify & Reduce
Use CAS to simplify:
Simplify[(x^2 - 9)/(x - 3)]
Then try:
Simplify[(x^2 - 4x + 4)/(x - 2)]
What happens? What assumptions is CAS making? When is the simplified form not valid?
Factor First, Then Simplify
Use:
Factor[x^2 - 9]
Factor[x^2 - 4x + 4]
Then:
(x^2 - 4x + 4)/(x - 2)
Why is factoring useful before simplifying? Could students reach incorrect conclusions if they skip domain analysis?