Question

Need help with Partial fraction decomposition

x^2 + 1
-----------------
x^3 + x^2 - 5x + 3

Which I turned into

x^2 + 1
---------------
(x-1)^2(x+3)

Answer 1

Any ideas on what do I do now since I never did it with an addition of a numerator?

Thanks,

Answer 2

=x3+x2−5x+3 EASY PEASY!

Answer 3

Hmmmm

I would need to find them in a A = , B = , C =

So it may be

x^2 + 1 = A B C
------ ----- + ------ + ---------
denom. x+ 3 x - 1 (x-1)^2

Answer 4

x^2 + 1 = A(x-1)^2 + B(x+3)(x-1) + C(x1)

Answer 5

go to math papa and press algebra calculator it will giive u the answer and explain step by step how it got the answer!:)

Answer 6

That's not much help, can you just double check if I'm right?

I made a mistake

it's x^2 + 1 = A(x-1)^2 + B(x-1)(x+3) + C (x+3)

Answer 7

x = 1, cancel A and B

2 = C(1+3)

2 = 4c

1/2 = C

Answer 8

x = -3

Cancel B and C

10 = 16A

10/16 = A

5/8 = A

Answer 9

x = 0

1 = 5/8 -3B + 3/2

1 = 19/8 - 3B

1 - 19/8 = -3B

-11/24 = B

Answer 10

Okay, so you're looking to turn
\(\Huge \frac{x^2 + 1 }{x^3 + x^2 - 5x + 3}\)
into a partial fraction decomposition.
Now, you factored, to get
\(\Huge \frac{x^2 + 1 }{(x-1)^2(x+3)}\)
You want to get something like this
\(\Huge =\frac{A }{(x-1)^2}+\frac{B }{(x-1)}+\frac{C }{(x+3)}\)
Now, to solve for the coefficients, I see you are using the heaviside cover up method. That is fine for the two non repeated terms, (x-1) and (x+3), but you will have to do the linear system for the first repeated term.

Answer 11

Usually in this case, since the heaviside cover up method isn't completely applicable, I'd prefer to just solve this as a system of three equation in 3 variables

Answer 12

5 -11 1
- ---- ----------
8 24 2
----- + ------- + -----------------
x + 3 x - 1 (x-1)^2

Answer 13

Your term for B is incorrect.

Answer 14

Crap, any solution for B?

Answer 15

9
- ---???
24

Answer 16

Here, let me upload a solution.

Answer 17

Since

1 = 5/8 -3B + 3/2

-9/8 = -3B

9/24 = B

oops it's positive

Answer 18

3/8

Answer 19

Looks good now.

Answer 20

http://www.wolframalpha.com/input/?i=partial+fractions+(x%5E2+%2B+1)%2F(x%5E3+%2B+x%5E2+-+5x+%2B+3)

Answer 21

HI

Answer 22

hi