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.