SOLUTION: Perform the division x3 -1/x2+x+1

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Question 1199368: Perform the division x3 -1/x2+x+1
Answer by ikleyn(52788) About Me  (Show Source):
You can put this solution on YOUR website!
.

Well known identity is

    x%5E3-1 = %28x-1%29%2A%28x%5E2%2Bx%2B1%29.


From this identity,

    %28x%5E3-1%29%2F%28x%5E2+%2B+x+%2B+1%29 = x-1.


ANSWER.  %28x%5E3-1%29%2F%28x%5E2+%2B+x+%2B+1%29 = x-1.

Solved.


For this identity,   x%5E3-1 = %28x-1%29%2A%28x%5E2%2Bx%2B1%29,   see the lesson
    - The difference of cubes formula.
in this site.

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Alternatively,  you may divide using long division.

The answer will be the same.