Your substitution is off . . .
I found the following relations:
Use partial fractions: .
. . I got: .
And checking out if we have 4t instead of 2t...
We have 4t=A(t-3)(t*t+1)+B(t-1)(t*t+1)+(Ct+D)(t-1)(t-3)
Substitute your A, B, C and D.
And then take t as 2, you can see that they are not equal.
If you take t as 100, they are equal.
I dont get the point.
to complex to be done reliably so doing it mechanicaly what you should end
up with is shown in the attachment.
This is what soroban gets for this, but with a factor of 2 rather than 4.
The partial fraction expansion is also shown in the attachment, but this
is again different from your book