Which one have you been writing?
Without further adieu (wrong)
Without further ado (right)
The idiom "without further ado" is a commonly used expression, signaling the speaker's intention to proceed with a task or topic without unnecessary delay or ceremony. It implies a desire to move forward promptly, skipping any additional formalities or unnecessary steps. The term "ado" in this context refers to fuss, bother, or unnecessary activity, emphasizing a straightforward approach.
On the other hand, "without further adieu" is a common misinterpretation. It likely arises from mishearing the original expression. The word "adieu" is a French term meaning farewell or goodbye. Mistakenly using this word in place of "ado" alters the intended meaning of the expression by introducing a farewell connotation rather than emphasizing a desire to avoid delay.