Algebra

Why is the correct answer a^2-a+1 to this problem:

a^3+1/a+1

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  1. Because a^3 + 1 factors to
    (a+1)(a^2 - a + 1)

    so

    (a^3+1)/(a+1) , notice the necessary use of brackets
    = (a+1)(a^2 - a + 1) / (a+1)
    = a^2 - a + 1, on the condition that a≠ -1

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