# In partial fractions, why must the degree of the numerator be lower than the denominator?

Specifically, it must be one degree lower. But why must it be smaller?

• It's not necessary, but maybe it's more comforting. – Michael Rozenberg Sep 28 '17 at 9:39
• I don't think so. Every textbook and video says it must be smaller. – Jane Doe Sep 28 '17 at 10:45
If you ever have a fraction where the degree of the numerator is not lower, then you could use long division to get simpler fractions. For example, $\dfrac{6x^2+3}{2x^2-x+7}=3+\dfrac{3x-18}{2x^2-x+7}$.
This is analogous to the "improper" fractions of positive integers being those where the numerator is not smaller than the numerator. $\dfrac{11}{3}=3+\dfrac{2}{3}$, etc.