1) It's a standard technique when you have repeated factors, because it's possible for a quadratic denominator to have up to a linear numerator rather than constant.

2) Again, quadratic denominators can have up to linear numerators. So you need to take into account that you need a linear function in the numerator.

Generally, to have algebraic proper fractions, the numerator can be any degree up to one less than the denominator's degree.