Partial Fraction Decomposition

[jmason52]

I am just coming back to math after a, oh 30 year or so, vacation. In the class I'm taking, we are studying Partial Fraction Decomposition ( Px/Qx:Qx). It doesn't entirely make sense to me, tho like a monkey typing the great American novel, I can solve them given enough time. I am just having trouble getting my hands around the overall concept, and I think what's missing is the why: What exactly are they used for, and will I see them again in calculus or DE or anytime soon? I am hoping that if I can understand the why, the how will become easier. Thanks in advance.

 

[VKint]

The main thing I've seen partial fractions used for is in evaluating complicated integrals. If you don't remember exactly what evaluating an integral entails, it's enough to understand that integrating something like (x^3 + 3x^2 - 1) / (x^4 - x + 2) without using partial fractions would be extremely painful (in fact, I'm not sure I could do it without PFs). If you can reduce a rational function to a sum of terms of the form A / (Cx + D) and others of the form (Ax + B) / (Cx^2 + Dx + E), then the integral becomes straightforward (it's just a sum of logarithms and inverse tangents).

 

[jmason52]

Thanks ! :)

I'm just starting the path, taking precalculus algebra, so I haven't been formally introduced to integrals just yet. I ran across Partial fractions in the section we're studying now on linear equations. The book doesn't really say anything about what they're used for, it just sticks a section in right between sections on equations with 2 and equations with 3 variables. The teached skipped over it entirely. So I learned how to do them on my own, but still needed the explanation. This helps a lot.