Please correct this:?

It becomes wrong when moving from the fourth line to the fifth, changing (x+1)(x-1)=x-1 to x+1=1. While normally you would be able to do this, you cannot in the specific case where x=1, since that would make the denominator 0, and you cannot divide by zero. The only reason you have been able to set x^2-1=x-1 in the first place is taking the specific instance in which x=1, so you must ume that in all cases along the way.