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

Question

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

Charlize Manning · Accepted Answer

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  +  Bfrom which       B    =    0  Making   s  =  0 in   (  1  ) gives  0  =  A  +  Cfrom which       C    =    −    1

Banguizb · Accepted Answer

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

How do you solve B and C for s − 1 </mrow>

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