Un-Simplifying a fraction, i.e. computing partial fraction decomposition 3 x 2 + 17 x x 3 + 3 x 2 + − 6 x − 8 I need to find the value of C in the form of A x + 1 + B x − 2 + C x + 4 which is based on the fraction give at the top.I can get so far to do the following: A ( x 2 + 2 x − 8 ) + B ( x 2 + 5 x + 4 ) + C ( x 2 − x − 2 ) = 3 x 2 + 17 xNo clue on my next step or even if this is the right step.

Question

Un-Simplifying a fraction, i.e. computing partial fraction decomposition            3              x        2            +      17      x                      x        3            +      3              x        2            +      −      6      x      −      8      I need to find the value of C in the form of       A          x      +      1        +      B          x      −      2        +      C          x      +      4       which is based on the fraction give at the top.I can get so far to do the following:  A  (      x    2    +  2  x  −  8  )  +  B  (      x    2    +  5  x  +  4  )  +  C  (      x    2    −  x  −  2  )  =  3      x    2    +  17  xNo clue on my next step or even if this is the right step.

tatovihd1 · Accepted Answer

(          A          +          B          +          C          )                          x          2                                    =        3                  x          2                                              (          2          A          +          5          B          −          C          )                x                            =        17        x                            −        8        A        +        4        B        −        2        C                            =        0            Dividing the first equation by       x    2   and the second by x will get you a linear system of equations.

tinydancer27br · Accepted Answer

A  (      x    2    +  2  x  −  8  )  +  B  (      x    2    +  5  x  +  4  )  +  C  (      x    2    −  x  −  2  )  =  3      x    2    +  17  x  .Setting   x  =  −  4   0  A  +  0  B  +  18  C  =  −  20.

Un-Simplifying a fraction, i.e. computing partial fraction decomposition 3

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