Alright, Im here again with another question....(adsbygoogle = window.adsbygoogle || []).push({});

When I have a rational function, let's say (x+4)/(x-2)(x-3) I rewrite it like A/(x-2) + B(x-3) and then solve it for A & B. But when we have for e.g (x^2 + 3x + 2)/(x(x^2 +1 )) the book tells me to rewrite it like:

A/x + (Bx + C)/(x^2 + 1), and then solve for A & B. I understand that the term x^2 +1 cannot be further decomposed (at least not if we only consider real numbers). However feel I don't get everything.

For example if I instead try to rewrite it on the form A/x + B/(x^2 + 1), so A(x^2 + 1) + Bx = x^2 +3x + 2, so A = 1, B = 3, and A = 2, which is of course impossible. On the other hand I can see that the other form described above (which the book tells me to use) works fine.

The problem is that with different rational functions I might be able to try different strategies and just see which one works out, but I feel i don't understand it the way I want to. In the book they simply say "the rational function P(x)/Q(x) can be expressed as a sum of partial fractions like this: .... but we don't explain it further cuz this is not a course in algebra" I feel I need to really understand, not just memorize the techniques!

Thanks for help!

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Partial fraction decomposition

**Physics Forums | Science Articles, Homework Help, Discussion**