Help to simplify this complicated fractionI require help to simplify this. I used the method to make the denominator a single fraction then multiply the top by the reciprocal but when it comes to cancelling, I'm not sure if i've done it right. 1 x 2 + x + 2 1 + 2 x ( x 2 + x + 2 )

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Help to simplify this complicated fractionI require help to simplify this. I used the method to make the denominator a single fraction then multiply the top by the reciprocal but when it comes to cancelling, I&#039;m not sure if i&#039;ve done it right.            1                                    x            2                          +        x        +        2                    1      +              2                  x          (                                    x              2                                +          x          +          2          )

Killaninl2 · Accepted Answer

Assuming   x  ≠  0 and       x    2    +  x  +  2  ≠  0 (the latter is always the case):            1                                    x            2                          +        x        +        2                    1      +              2                  x          (                                    x              2                                +          x          +          2          )                      ⋅            x      (              x        2            +      x      +      2      )              x      (              x        2            +      x      +      2      )        =      x          x      (              x        2            +      x      +      2      )      +      2      It is not possible to simplify this further, if not by factorizing the denominator. Please keep in mind the conditions I&#039;ve put in the beginning.EDIT: factorization leads to the final answer:      x          (      x      +      1      )      (              x        2            +      2      )      Only for non-zero   x; now that you&#039;ve got an explicit form of the fraction, you can put existence conditions. In this case,   x  ≠  0 and   x  ≠  −  1

jlo2ni5x · Accepted Answer

1                                    x            2                          +        x        +        2                    1      +              2                  x          (                                    x              2                                +          x          +          2          )                      =      x          x      (              x        2            +      x      +      2      )      +      2        =      x          (      x      +      1      )      •      (              x        2            +      2      )      where   x  ≠  −  1

I require help to simplify this. I used the method to make the denominator a single fraction then multiply the top by the reciprocal but when it comes to cancelling, I'm not sure if i've done it right. (1)/((x^2)+x+2)/(1+(2)/(x((x^2)+x+2)))

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