cambrassk3

cambrassk3

Answered

2022-07-03

How do you solve B and C for s 1 s + 1 s s 2 + 1 = A s + 1 + B s + C s 2 + 1 ?
A = s 2 s s 2 + 1 | s = 1 = 1 ( 1 ) 1 + 1 = 1

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Answer & Explanation

Charlize Manning

Charlize Manning

Expert

2022-07-04Added 12 answers

We have
(1) s 1 s + 1 s s 2 + 1 = A s + 1 + B s + C s 2 + 1
Multiplying ( 1 ) by s and making s gives
1 = A + B
from which B = 0
Making s = 0 in ( 1 ) gives
0 = A + C
from which C = 1

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Banguizb

Banguizb

Expert

2022-07-05Added 3 answers

Cross-multiplying on the right hand side gives
A s 2 + A + B s 2 + B s + C s + C on the numerator. Plug A = 1
( 1 + B ) s 2 + ( B + C ) s + ( 1 + C ) = s 2 s. Equate the coefficients
1 + B = 1 B = 0
B + C = 1 C = 1

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