Partial fraction decomposition

[kristopher0123]

Hey everyone...umm...yeah I'll just get right to it.

Question:
x^2-x+2
----------
x(x-1)^2

My work:
x^2-x+2
---------- =
x(x-1)^2

A_____B_____ C
--- + -------- + ---
x-1__(x-1)^2__x

I don't know where to go now since x^2-x+2 is unfactorable...or if that even matters. If you can help me, it would be greatly appreciated. Sorry about formatting issues. I don't know how to make it all nice and neat like all of you haha...

 

[daon]

You don't factor it. Multiply both sides by x(x-1)^2 and multiply it out. Collect like terms, equate coefficients of the powers of x to solve for A,B,C. It will be a linear system.

 

[kristopher0123]

Is there any chance you could show me an example?

 

[kristopher0123]

WAIT! Is there no solution???

 

[daon]

Just an example:

x/(x-2)(x-1) = A/(x-2) + B/(x-1)

Hence

x = A(x-1)+B(x-2)

x = (A+B)x + (-A-2B)

A+B = 1
-A-2B = 0

Solving this gives B=-1 and A=2.