(a) Except as provided by Subsection (b) or Section 152.801(a), all partners are jointly and severally liable for all obligations of the partnership unless otherwise:
(1) agreed by the claimant; or
(2) provided by law.
(b) A person who is admitted as a partner into an existing partnership does not have personal liability under Subsection (a) for an obligation of the partnership that:
(1) arises before the partner's admission to the partnership;
(2) relates to an action taken or omission occurring before the partner's admission to the partnership; or
(3) arises before or after the partner's admission to the partnership under a contract or commitment entered into before the partner's admission.