Find the partial fractions for the following:
3x² - 2x + 8
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x³ + 2x² + 4x + 8
9x² + 21x - 24
--------------------------
x³ + 4x² - 11x - 30
My biggest problem with these is that I have trouble factoring the bottom cubic in the second problem, but I'm having trouble with everything else also. Every time I try to solve the problems I end up with a different answer than the time before. I don't know what I am doing wrong!
I shall be eternally grateful to whoever helps me solve these problems. So grateful, in fact, that I shall bestow upon them this bear hug.
. . . Wow. It's obviously sleepy time for me. My true weirdness is oozing into your website. Terribly sorry about that.
If your problem had a 1 in the numerator, there's a nice formula to bypass messy algebra which I'll demonstrate in this specific case:
=
This formula works whenever you have a 1 in the numerator and linear factors in the denominator.