SOLUTION: Simplify the rational expression: x to the 3rd power - 1 ___________ ___________ __ 1-x

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Question 288479: Simplify the rational expression:
x to the 3rd power - 1
__________________________
1-x
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
%28x%5E3-1%29%2F%281-x%29
Recognize (x^3 - 1) as the difference of squares, which factors, so you have;
%28%28x-1%29%28x%5E2%2Bx%2B1%29%29%2F%281-x%29
Rewrite (1-x)
%28%28x-1%29%28x%5E2%2Bx%2B1%29%29%2F%28-1%28x-1%29%29
cancel (x-1)
%28x%5E2%2Bx%2B1%29%2F-1 = -%28x%5E2%2Bx%2B1%29