(1/1-х2)+((х^2+х+1)(х^2-х+1)/(х^6-1)

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вопрос

To simplify the expression, we need to factor the denominators of each fraction and then combine them by finding a common denominator.

Given expression:

(1/(1-x^2)) + ((x^2 + x + 1)(x^2 - x + 1)) / (x^6 - 1)

First, factor the denominator x^6 - 1 using the difference of squares formula:

x^6 - 1 = (x^3 + 1)(x^3 - 1)
= (x^3 + 1)(x+1)(x^2 - x + 1)

Now, rewrite the expression with a common denominator:

(1/(1-x^2)) + (((x^2 + x + 1)(x^2 - x + 1)(x+1)) / ((x^3 + 1)(x+1)(x^2 - x + 1)))

Simplify the expression by canceling out common factors:

(1/(1-x^2)) + ((x^2 + x + 1)/(x^3 + 1))

Therefore, the simplified form of the expression is:

1/(1-x^2) + (x^2 + x + 1)/(x^3 + 1)