Nathanial Levine

2022-10-01

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?

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

Frida King

Beginner2022-10-02Added 8 answers

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, $\frac{6{x}^{2}+3}{2{x}^{2}-x+7}}=3+{\displaystyle \frac{3x-18}{2{x}^{2}-x+7}$.

This is analogous to the "improper" fractions of positive integers being those where the numerator is not smaller than the numerator. $\frac{11}{3}}=3+{\displaystyle \frac{2}{3}$, etc.

This is analogous to the "improper" fractions of positive integers being those where the numerator is not smaller than the numerator. $\frac{11}{3}}=3+{\displaystyle \frac{2}{3}$, etc.

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