I really hate this method. Think about it.
1) Initially, the value you are about to substitue is NOT in the Domain.
2) If it IS in the Domain, you are about to multiply things by zero (0).
3) Why does this make sense?
On the other hand, one cannot deny that it works.
Your last trick shoud result in:
D + E = 0
D - E = 1
Solving the system produces the desired result.