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let
1/[(t^2-1)(t+1)] ≡ A/(t+1) +B/(t+1)^2 +C/(t-1)
=>
1≡ A(t+1)(t-1) +B(t-1) +C(t+1)^2
t=-1, =>B=-1/2
coef. of t
B+2C =0
-1/2+2C=0
C=1/4
coef. of t^2
A+C = 0
A=-1/4
ie
1/[(t^2-1)(t+1)] ≡ -(1/4)[1/(t+1)] -(1/2)[1/(t+1)^2] +(1/4)[1/(t-1)]
1/[(t^2-1)(t+1)] ≡ A/(t+1) +B/(t+1)^2 +C/(t-1)
=>
1≡ A(t+1)(t-1) +B(t-1) +C(t+1)^2
t=-1, =>B=-1/2
coef. of t
B+2C =0
-1/2+2C=0
C=1/4
coef. of t^2
A+C = 0
A=-1/4
ie
1/[(t^2-1)(t+1)] ≡ -(1/4)[1/(t+1)] -(1/2)[1/(t+1)^2] +(1/4)[1/(t-1)]
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