Partial fractions - alternative resultI have the following fraction: z ( z − 1 ) ( z − 2 ) When I try to decompose it to partial fractions, I get: − 1 z − 1 + 2 z − 2 But the result in my book is: − z z − 1 + z z − 2 Both results are correct, but, how am I supposed to get the second one?

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Partial fractions - alternative resultI have the following fraction:      z          (      z      −      1      )      (      z      −      2      )      When I try to decompose it to partial fractions, I get:  −      1          z      −      1        +      2          z      −      2      But the result in my book is:  −      z          z      −      1        +      z          z      −      2      Both results are correct, but, how am I supposed to get the second one?

hildiadau0o · Accepted Answer

I agree with the comments that the result stated in the back of the book is somewhat non-standard. The way that you can see that the two results are the same is by cleverly adding and subtracting 1.                                          −            1                                z            −            1                          +                  2                      z            −            2                                              =                              −            1                                z            −            1                          −        1        +                  2                      z            −            2                          +        1                                          =                              −            1                                z            −            1                          −                              (            z            −            1            )                                z            −            1                          +                  2                      z            −            2                          +                              z            −            2                                z            −            2                                                            =                              −            z                                z            −            1                          +                  z                      z            −            2

arridsd9 · Accepted Answer

z          (      z      −      1      )      (      z      −      2      )        =            z      (      z      −      1      )      −      z      (      z      −      2      )              (      z      −      1      )      (      z      −      2      )        =  .  .  .

Partial fractions - alternative result I have the following fraction: z (

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