Question

decompose x^4 - x^3 - 2x^2 + 4x - 3 / x(x-1)^2 into partial fractions.

Answer 1

hint:

your denominator is x(x-1)^2 so your PF. would look something like \[\frac Ax + \frac B{x-1} + \frac C{(x-1)^2}\]
does that help?

Answer 2

hmmm...
you have to divide first, because the degree of the denominator is less than the degree of the numerator

Answer 3

lol..didn't see that

Answer 4

so I must first do long division?

Answer 5

yes, this problem pretty much sucks, because there is no avoiding the long division
i would cheat
http://www.wolframalpha.com/input/?i=%28+x^4+-+x^3+-+2x^2+%2B+4x+-+3+%29%2F+%28x%28x-1%29^2%29

Answer 6

How do i know that in this case the degree of the the Denominator is more than the degree of the numerator?