I have often heard it said that complex analysis is in some ways simpler than real analysis (because every differentiable function can be differentiated as many times as we want, and always has a power series expansion). Similarly, many theorems in projective geometry are simpler than their equivalents in euclidean geometry because one doesn't have to deal with the exceptional case of non-intersecting lines.
Are there any other well-known pairs of mathematical topics that bear a similar relationship, where theorems are greatly simplified by the removal of an exceptional case?
One example I encountered recently is elliptic geometry as a simplification of spherical geometry. By equating antipodal points, one is able to state “two distinct points make a line” without having to include an exception for the case where the two points are opposite one another on the sphere (such points would no longer be considered distinct).