Need some insight into how to determine A, C, and D
(x^2 - 2x - 1) /(((x - 1)^2)(x^2 + 1)
A / ( x - 1) + B / (x - 1)² + (Cx +D) / (x² + 1)
x² - 2x - 1 = A(x - 1 )(x² + 1) - (x² +1) + (Cx + D)(x - 1)²
Now I know that B = -1. What i'm having trouble is figuring out the others. I've tried foiling out everything but then when I equate coefficients, i'll have two variables equal to each other. Any help is appreciated (Worried)
So the remaining challenge is to descompose
That was pretty confusing but after studying it, it makes perfect sense. I appreciate it
Question. You foiled everything out but is there a simpler method to do this without expanding everything? I'm asking because the professor told us we can use three methods : Finger method, Equating Coefficients, and plugging an arbitrary value for X to solve for A, B, C, and D.
I was wondering if you could show me using the last method perhaps?
In your first line, I thought since B = -1 it's supposed to be - (x^2 + 1)? Or is there a rule where we don't put in the -1?
Edit : I'm even more lost by that last method. If you have three variables in one equation, how are you supposed to know each one?
you have -6 = 5A + 2C + D. How am I supposed to get those variables from here? Thanks and sorry for the many questions.
I made some typos... I edited it (Wink)
Originally Posted by JonathanEyoon
I'm sincerely sorry for the confusion ! (Bow)
For example, from (2), you have A=D.
Then, substitute in (1) and (3), etc...
You have to solve this system :
These (1), (2) & (3) label equations :p
Ah ic what you mean now. I'll give it a try!