How to simplify this fraction with different powers?I happen to be stuck trying to simplify this: [ ( 3 x + 2 ) ( x + 1 ) 3 2 − ( 3 2 x 2 + 2 x ) ( 3 2 ) ( x + 1 ) 1 2 ( x + 1 ) 3 ]

Question

How to simplify this fraction with different powers?I happen to be stuck trying to simplify this:      [                  (        3        x        +        2        )        (        x        +        1                  )                      3            2                          −        (                  3          2                          x          2                +        2        x        )        (                  3          2                )        (        x        +        1                  )                      1            2                                      (        x        +        1                  )          3                      ]

kregde84 · Accepted Answer

We have            (      3      x      +      2      )      (      x      +      1              )                  3          2                    −      (              3        2                    x        2            +      2      x      )      (              3        2            )      (      x      +      1              )                  1          2                            (      x      +      1              )        3            divide numerator and denominator by   (  x  +  1      )                  1        2             giving            (      3      x      +      2      )      (      x      +      1      )      −      (              3        2                    x        2            +      2      x      )      (              3        2            )              (      x      +      1              )                  5          2                    multiply the   (  3  x  +  2  )  (  x  +  1  ) to get   3      x    2    +  5  x  +  2 and the   (      3    2        x    2    +  2  x  )  (      3    2    ) to get       9    4        x    2    +  3  x giving:            3              x        2            +      5      x      +      2      −              9        4                    x        2            −      3      x              (      x      +      1              )                  5          2                    then simplify the numerator:  3      x    2    +  5  x  +  2  −      9    4        x    2    −  3  x  =      12    4        x    2    −      9    4        x    2    +  5  x  −  3  x  +  2  =      3    4        x    2    +  2  x  +  2to get                    3        4                    x        2            +      2      x      +      2              (      x      +      1              )                  5          2

demitereur · Accepted Answer

(      3      x      +      2      )      (      x      +      1              )                  3          2                    −      (              3        2                    x        2            +      2      x      )      (              3        2            )      (      x      +      1              )                  1          2                            (      x      +      1              )        3              =take the common factor   (  x  +  1      )          1      2        =            [      (      3      x      +      2      )      (      x      +      1      )      −      (              3        2                    x        2            +      2      x      )      (              3        2            )      ]              (        x        +        1                  )                      1            2                                      (      x      +      1              )        3              =  =            (      3      x      +      2      )      (      x      +      1      )      −      (              3        2                    x        2            +      2      x      )      (              3        2            )              (      x      +      1              )        3                    (        x        +        1                  )                      −                          1              2                                            =            (      3              /            4      )              x        2            +      2      x      +      2              (      x      +      1              )                              5            2

I happen to be stuck trying to simplify this: [((3x+2)(x+1)^(3/2)-(3/2x^2+2x)(3/2)(x+1)^(1/2))/(x+1)^3]

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