Tenants broke up and girlfriend refuses to leave the house

[David Eyal]

Hi all, 

I have a couple with 2 kids living in my property, it's time to renew the lease after they have been living there for more than 2 years.

The male tenant says he wants to be on the lease by himself as they broke up and he asked her to leave, but the problem is that she refuses to leave. 

He is a great tenant, i don't mind extending the lease with him, but if she refuses to leave he won't stay.

1. Should i sign him and ask her to leave? she cannot pay rent by herself.

2. Should i ask them both to leave and look for other family?

thanks