A partnership can be joined by:

A) investing into the business.
B) purchasing an equity interest in the business.
C) buying out one of the partners and taking over their interest (by mutual agreement) .
D) All of the above are correct.

All the options provided are valid ways to join a partnership. Investing in the business, purchasing an equity interest, or buying out an existing partner's interest with mutual agreement are all common methods for becoming a partner in a partnership.