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What should one teach to liberal-arts students who will take only one math course, and that because it's required of them?

The conventional answer: partial Partial fractions. And various useless clerical skills that they'll need if they take second-year calculus, although they'll never take first-year calculus. Et cetera.

E.g. in third grade you were told that $$3+3+3+3+3 = 5+5+5$$ and so on. Why should that be true? Assign that as a homework problem. At this point they may think that means there's some formula to plug this information into to get the answer. They've been taught that memorizing algorithms and applying them is what math is. That's a lie. We should stop lying and level with them.
E.g. in third grade you were told that $$3+3+3+3+3 = 5+5+5$$ and so on. Why should that be true? Assign that as a homework problem. At this point they may think that means there's some formula to plug this information into to get the answer. They've been taught that memorizing algorithms and applying them is what math is. That's a lie. We should stop lying and level with them.