Partial Fractions Concept check

frank789

Junior Member
Joined
Sep 16, 2017
Messages
58
Hi all,

apologize for my ignorance have a quick question:

when I decompose into partial fractions, if I have a single quadratic factor such as x^2, i have to account for factors x and x^2. im good with that.

when i solve for my partial fractions i would then have

a/x + b/x^2

perhaps im doing this wrong but with the x^2 being a quadratic factor, why does it not require a numerator of bx + c? or does it and i am confused? a quick proof would really make my monday.

thanks!
 
Hi all,

apologize for my ignorance have a quick question:

when I decompose into partial fractions, if I have a single quadratic factor such as x^2, i have to account for factors x and x^2. im good with that.

when i solve for my partial fractions i would then have

a/x + b/x^2

perhaps im doing this wrong but with the x^2 being a quadratic factor, why does it not require a numerator of bx + c? or does it and i am confused? a quick proof would really make my monday.

thanks!
This is good thinking. If you were to use ONLY x^2, you would need bx+c. You are just splitting it out ahead of time.

\(\displaystyle \dfrac{bx+c}{x^{2}} = \dfrac{bx}{x^{2}} + \dfrac{c}{x^{2}}= \dfrac{b}{x} + \dfrac{c}{x^{2}}\)

They are equivalent forms.

The direct answer to your question is, "You already covered it when you used x and x^2, separately."
 
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