First, the do-not-end-a-sentence-with-a-preposition rule appears to originate from the 17th Century Latin-variance coined by John Dryden (1631-1700) in 1627 (Greene 2011). He argued that English required conformity from Latin, which rejects any leniency of end-of-a-sentence-with-a-preposition (Greene 2011; Lowth 1794, 104).
Then Bishop Robert Lowth (1710-1787) continued the rejection of end-of-a-sentence-with-a-preposition as a Latin-based argument in 1762, which he coined the phrase, “…solemn and elevated style” (Lowth 1794, 127-128). English required a severe aversion from non-Latin construction under his point-of-view as it were below any such proper distinction, which appears to be a rejection of commonality of practice (i.e., Rejection of poorer-to-middle classes’ use of “proper speech”).
Second, the do-not-split-an-infinitive rule by Edmund Spenser (ca. 1552/1553-1599), John Dryden, and Alexander Pope (1688-1744), which was a rejection of Middle English use of Germanic origin as opposed to Latin origination (Hall 1882; cf. Schuster 2003). As with the previous rule, these writers argued that English required Latin-basis as any variant to the contrary would debase the language entirely (Hall 1882).
Both rules appear to be a class-based separation, or instead, an additional requirement of Latin-centric academic writing for their commonplace. In other words, if someone attempts to correct your grammar as a violation of either grammatical faux pas, gently remind them that English is a German-based variant, not a Latin-centric framework.
Therefore, feel free to end any sentence with a preposition or split an infinitive as German freely allows for either rule liberally implemented under grammatical syntax (Hall 1882).
Greene, Robert Lane. “Three Books for the Grammar Lover in Your Life: NPR.” NPR. Retrieved April 15, 2018.
Hall, Fitzedward (1882). “On the Separation, by a Word or Words, of to and the Infinitive Mood.” American Journal of Philology. The Johns Hopkins University Press. 3 (9): 17–24. Retrieved April 15, 2018.
Lowth, Robert. (1794). A Short Introduction to English Grammar: With Critical Notes [EBook, Google]. Retrieved April 15, 2018.
Schuster, Edgar H. (2003) Breaking the Rules: Liberating Writers Through Innovative Grammar Instruction [EBook, Google]. Retrieved April 15, 2018.