# 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?

Nathanial Levine 2022-10-01 Answered
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?
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Frida King
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, $\frac{6{x}^{2}+3}{2{x}^{2}-x+7}=3+\frac{3x-18}{2{x}^{2}-x+7}$.
This is analogous to the "improper" fractions of positive integers being those where the numerator is not smaller than the numerator. $\frac{11}{3}=3+\frac{2}{3}$, etc.