If the bible is the inerrant word of god, how do Christians reconcile the obvious edits to the word?

Example: Remember that inspiring story about Jesus and the adultress? He that is without sin among you, let him first cast a stone at her?
NEVER happened, even in the context of the NT as a true history.
In the oldest Greek manuscripts, this story doesn't appear. It was added in later versions.

What's up with that?