The domain is the numbers you can put in for the variable. When you canceled off the factor and got rid of a zero you put that zero back into the allowed values. To be the same as you started with you have to take that value back out so you have the same numbers you can put in as you started with.What does it mean to 'change the domain'?
Just like the links showed. That's why you have to put the restrictions back in (take the zeros back out) so you don't change what the expression is.How can a simplification of an equation change what it equals?