# Partial Fractions

• Jan 30th 2009, 10:56 AM
i_cow044
Partial Fractions
Hello, I was wondering if anyone can help me with this problem. Im fine with most partial fraction problems but this one has me kinda stumped. Can you help, the problem is below.

x^2 -3X +6/x(x -2)(x -1)

They want this seperated into partial fractions. I dont know what I'm doing wrong, but anytime i multiply out the factors so that I can divide the numerator I end up screwing it up. I know the answer I looked in the back of the book it should be 3/x +2/(x -2) - 4/(x -1). Unless the book is wrong.

I've been wracking my brains for an hour trying to figure this out and keep coming up with wrong answers. Anyhelp would be really appreciated.

Thank you
• Jan 30th 2009, 11:10 AM
running-gag
Hi

$\frac{x^2-3x+6}{x(x-1)(x-2)}=\frac{a}{x}+\frac{b}{x-1}+\frac{c}{x-2}$

Multiple both sides by x
$\frac{x^2-3x+6}{(x-1)(x-2)}=a+\frac{bx}{x-1}+\frac{cx}{x-2}$

Then set x to 0
$\frac{6}{2}=a$

Multiply both sides by (x-1)
$\frac{x^2-3x+6}{x(x-2)}=\frac{a(x-1)}{x}+b+\frac{c(x-1)}{x-2}$

Then set x to 1
$\frac{4}{-1}=b$

etc