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Applicable only in academic settings. Every problem the professor goes over in class will have a clean solution. It is most likely that professors design their lectures that way to make it easy to illustrate a concept without getting bogged down in silly details. Similarly for problem sets: the idea is for you to learn the concepts, not practice complicated algebra or long division. This principle also allows you to check your algebra just by plugging in some random number -- say 4.2 -- for x on both sides. If both sides then evaluate to the same number, you're probably okay.

The contrapositive is that if you're doing a problem, and it looks like it's getting really messy with annoying fractional coefficients or whatever, you're probably doing something wrong.

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