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.