What is the legitimate Islamic ruling regarding the method of dividing profits and losses among partners in business, especially when one partner withdraws a portion of the capital and the impact of that on profits and expenses?

The contract between you is invalid because the partnership is not permissible when the compensation is not in cash, and because Mudarabah (profit-sharing partnership) requires specifying a known percentage of the profit for each party, and because the rent of the premises and operating costs are deducted from the Mudarabah capital, not from the profit. The entire profit belongs to the owner of the capital, and the worker is entitled to the wage of the like (Mithl).