Partial fraction in two variable problemHow to write partial fraction of 12 m − n − 3 m n + 7 5 m − 2 n − 2 m n + 5 I just write first and second denominator: 5 − 2 n and m + 1

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Partial fraction in two variable problemHow to write partial fraction of            12      m      −      n      −      3      m      n      +      7              5      m      −      2      n      −      2      m      n      +      5      I just write first and second denominator:   5  −  2  n and   m  +  1

Ryan Fitzgerald · Accepted Answer

The deg on top and bottom are the same. Before we do the partial fraction thing we should do division I believe. So the division part:             12      m      −      n      −      3      m      n      +      7              5      m      −      2      n      −      2      m      n      +      5        =                    3        2            (      −      2      m      n      +      5      −      2      n      +      5      m      )              5      m      −      2      n      −      2      m      n      +      5        +            −              1        2            +      2      n      +              9        2            m              5      m      −      2      n      −      2      m      n      +      5       ... Now preparing for the partial fraction part...   −  2  m  n  +  5  −  2  n  +  5  m  =  −  2  m  n  +  2  n  +  5  +  5  m  =  −  2  n  (  m  +  1  )  +  5  (  m  +  1  )  =  (  m  +  1  )  (  5  −  2  n  )                              −          1                2            +      2      n      +              9        2            m              (      m      +      1      )      (      5      −      2      n      )        =      A          m      +      1        +      B          5      −      2      n        giving us             −      1        2    +  2  n  +      9    2    m  =  A  (  5  −  2  n  )  +  B  (  m  +  1  ) Expanding...             −      1        2    +  2  n  +      9    2    m  =  −  2  A  n  +  5  A  +  B  m  +  B  =  −  2  A  n  +  B  m  +  (  5  A  +  B  ) Now compare both sides:   2  =  −  2  A  ;  B  =      9    2    ;  5  A  +  B  =            −      1        2   You should end up with       3    2    +            −      1              m      +      1        +            9      2              5      −      2      n

Dania Mueller · Accepted Answer

HINT:            12      m      −      n      −      3      m      n      +      7              5      m      −      2      n      −      2      m      n      +      5        =            12      m      −      n      −      3      m      n      +      7              (      m      +      1      )      (      5      −      2      n      )        =      A          m      +      1        +      B          5      −      2      n        =            A      (      m      +      1      )      +      B      (      5      −      2      n      )              (      m      +      1      )      (      5      −      2      n      )      where   A  ,  B are constants to be determined.So we can write that  A  (  m  +  1  )  +  B  (  5  −  2  n  )  =  12  m  −  n  −  3  m  n  +  7Can you proceed now?

Partial fraction in two variable problem How to write partial fraction of 12

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