using the method of partial fractions obtain the expansion of

1-s/ s^2(s^2+1)

Im not sure how to go about it as you cant factorise the s^2+1

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- Nov 22nd 2006, 03:16 PMfeage7partial fraction question
using the method of partial fractions obtain the expansion of

1-s/ s^2(s^2+1)

Im not sure how to go about it as you cant factorise the s^2+1 - Nov 22nd 2006, 03:58 PMThePerfectHacker
- Nov 22nd 2006, 08:52 PMCaptainBlack
- Nov 23rd 2006, 04:27 AMfeage7
- Nov 23rd 2006, 04:37 AMCaptainBlack
- Nov 23rd 2006, 05:18 AMfeage7
Im just going wrong everywehre

When i put i in i get

1-i = (Ci+D)(i)(-1)

1-i = (-c+Di)(-1)

1-i = C-Di

so i get C=1 and D = 1 which isnt right

aslo when i do A and B i end up with

1-s= As^4 + As^2 = Bs^3 +Bs + Cs^4 + Ds^3

equating terms in s gives me B=-1 and equating either s^4 or s^2 gives me A as 0 - Nov 23rd 2006, 06:10 AMtopsquark

=

So:

Thus

A + C = 0

B + D = 0

A = -1

B = 1

So

C = 1

D = -1

Thus:

================================================== ==

In terms of the complex denominators:

=

So:

Thus:

A + C + D = 0

B - iC + iD = 0

A = -1

B = 1

So

C + D = 1

-iC + iD = -1

So

C = (1/2)(1-i)

D = (1/2)(1+i)

Thus:

-Dan