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!

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# Partial fraction decomposition

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