Two domains sharing one User/Member database


I have two domains, but they have to share one User/Member database so when a person becomes a Member, they become a Member on both sites and I only have to set up the Membership tiers once and they will apply to both sites, and when a Member logs into one site, they’re logged into the other site as well. The two sites have completely different content and themes, so I only want to share the User/Member database. I already have the two databases installed on the one domain, but the instructions I have to alter $wpdb->prefix = $table_prefix; applies to WP 2, and the code referenced there doesn’t exist in WP 3.8.1. I haven’t gotten past that point so I don’t know if the rest of the instructions I have will apply to 3.8.1 either.

How do I accomplish sharing the User/Member database between the two domains in WP 3.8.1?