dividing fractions with X

Question

I divided 1/3x^3 -X +C by (x-1) 

 

and I got (x^3 -X +C)/3x-1. 

 

my book shows the answer as (x^3 -3X +C)/3x-1. 

 

why are they multiplying the x by 3?

 

Answer 1

Divide 1/3 x³ - x + c  by ( x- 1 )

 

By long division:

 

             1/3 x² + 1/3 x  - 2/3 + (-2/3 + c)/ (x-1)

x - 1   √ 1/3 x³  + 0 x² - x  +  c

             1/3 x³ -1/3 x² 

 

                      1/3 x² - x

                      1/3 x² - 1/3 x

 

                                -2/3 x + c

                                -2/3 x + 2/3

 

                                          -2/3 + c

Answer 2

IMHO the book is wrong also!

(1/3)x³ - x + c = (x³ - 3x + 3c) / 3 

To divide by (x -1) multiply by 1 / (x - 1)

[(x³ - 3x + 3c) / 3] [1 / (x - 1)

(x³ - 3x + 3c) / 3(x - 1)