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
Answered 2022-10-02 Author has 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, 6 x 2 + 3 2 x 2 x + 7 = 3 + 3 x 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. 11 3 = 3 + 2 3 , etc.
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