SOLUTION: Hello all. I am to simplify the following polynomial using long division. {{{(x^3-1)(x^2-1)^(-1)}}} The book says that the answer is: {{{x+1/(x+1)}}} I do not know how the

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Hello all. I am to simplify the following polynomial using long division. {{{(x^3-1)(x^2-1)^(-1)}}} The book says that the answer is: {{{x+1/(x+1)}}} I do not know how the      Log On


   

Question 269372: Hello all.
I am to simplify the following polynomial using long division.
%28x%5E3-1%29%28x%5E2-1%29%5E%28-1%29
The book says that the answer is:
x%2B1%2F%28x%2B1%29
I do not know how the book came to that conclusion?
Can someone help please?
Thanks
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
I am to simplify the following polynomial using long division.
%28x%5E3-1%29%28x%5E2-1%29%5E%28-1%29
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= %28x%5E3-1%29%2F%28x%5E2-1%29
= +%28x-1%29%2A%28x%5E2%2Bx%2B1%29%2F%28%28x-1%29%2A%28x%2B1%29%29
= +%28x%5E2%2Bx%2B1%29%2F%28x%2B1%29
= +%28x%2A%28x%2B1%29+%2B+1%29%2F%28x%2B1%29
= +x%28x%2B1%29%2F%28x%2B1%29+%2B+1%2F%28x%2B1%29
= x+%2B+1%2F%28x%2B1%29