Decompose a fraction in a sum of twoLet's say that I have this fraction: 2 x x 2 + 4 x + 3 I would like to decompose in two fraction: A x + 3 + B x + 1 Which is the procedure for that? :)

Question

Decompose a fraction in a sum of twoLet&#039;s say that I have this fraction:            2      x                      x        2            +      4      x      +      3      I would like to decompose in two fraction:      A          x      +      3        +      B          x      +      1      Which is the procedure for that? :)

kaveljo49bl · Accepted Answer

2      x                      x        2            +      4      x      +      3        =            2      x                      x        2            +      x      +      3      x      +      3        =            2      x              x      (      x      +      1      )      +      3      (      x      +      1      )        =  =            2      x              (      x      +      3      )      (      x      +      1      )        =      A          x      +      3        +      B          x      +      1        2  x  =  A  x  +  A  +  B  x  +  3  B  =  (  A  +  B  )  x  +  A  +  3  BYou needs to solve the system  A  +  B  =  2  ,  A  +  3  B  =  0

Marlie Cole · Accepted Answer

x    2    +  4  x  +  3  =  0  Δ  =      4    2    −  4  ⋅  1  ⋅  3  =  4      x          1      ,      2        =            −      b      ±              Δ                    2      a        =            −      4      ±      2        2    =  −  3   or   −  1      x    2    +  4  x  +  3  =  (  x  +  3  )  (  x  +  1  )            2      x                      x        2            +      4      x      +      3        =            2      x              (      x      +      3      )      (      x      +      1      )        =      A          x      +      3        +      B          x      +      1        =            A      (      x      +      1      )      +      B      (      x      +      3      )              (      x      +      3      )      (      x      +      1      )        =            (      A      +      B      )      x      +      (      A      +      3      B      )              (      x      +      3      )      (      x      +      1      )      Since,             2      x              (      x      +      3      )      (      x      +      1      )        =            (      A      +      B      )      x      +      (      A      +      3      B      )              (      x      +      3      )      (      x      +      1      )       ,it must be:  A  +  B  =  2   and   A  +  3  B  =  0  A  +  3  B  =  0  ⇒  A  =  −  3  B  A  +  B  =  2  ⇒  −  2  B  =  2  ⇒  B  =  −  1  A  =  3Therefore:            2      x                      x        2            +      4      x      +      3        =      3          x      +      3        −      1          x      +      1

Decompose a fraction in a sum of two Let's say that I have this fraction: 2

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