Rabbi Eliezer employs one of the most powerful tools in the rabbinic interpretive arsenal: the gezeirah shavah, a comparison of two passages that share a common word. The word in question is "send," and its appearance in two different legal contexts creates a surprising legal link.
In the laws of servitude, the Torah states that a Hebrew servant who has been injured by his master must be sent free. The word used is a form of "send." Separately, in the laws of divorce (Deuteronomy 24:1), the Torah describes a husband who "sends" his wife from his house, which requires a written document, a get.
Rabbi Eliezer connects these two passages through their shared verb. Just as divorce requires a written document, so too the freeing of a servant requires a written document. The servant does not simply walk away. The master must produce a formal writ of emancipation, a document that legally terminates the relationship and certifies the servant's new status as a free person.
This interpretation has practical consequences. Without a document, the servant's freedom might be contested. Someone might claim the servant is still bound, still owned, still obligated. The writ eliminates all ambiguity. It is proof, permanent and portable, that the servitude has ended.
The gezeirah shavah method that Rabbi Eliezer uses here illustrates a core rabbinic conviction: the Torah is a single, unified text. A word that appears in Exodus and a word that appears in Deuteronomy are not coincidences. They are signals, deliberate echoes planted by the divine Author to ensure that one law illuminates another across the breadth of Scripture.