(1/1-х2)+((х^2+х+1)(х^2-х+1)/(х^6-1)
(1/1-х2)+((х^2+х+1)(х^2-х+1)/(х^6-1)
Не можешь разобраться в этой теме?
Обратись за помощью к экспертам
Гарантированные бесплатные доработки в течение 1 года
Быстрое выполнение от 2 часов
Проверка работы на плагиат
Поможем написать учебную работу
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−x2)1/(1-x^2)1/(1−x2) + (x2+x+1)(x2−x+1)(x^2 + x + 1)(x^2 - x + 1)(x2+x+1)(x2−x+1) / x6−1x^6 - 1x6−1
First, factor the denominator x^6 - 1 using the difference of squares formula:
x^6 - 1 = x3+1x^3 + 1x3+1x3−1x^3 - 1x3−1 = x3+1x^3 + 1x3+1x+1x+1x+1x2−x+1x^2 - x + 1x2−x+1
Now, rewrite the expression with a common denominator:
1/(1−x2)1/(1-x^2)1/(1−x2) + ((x2+x+1)(x2−x+1)(x+1))/((x3+1)(x+1)(x2−x+1))((x^2 + x + 1)(x^2 - x + 1)(x+1)) / ((x^3 + 1)(x+1)(x^2 - x + 1))((x2+x+1)(x2−x+1)(x+1))/((x3+1)(x+1)(x2−x+1))
Simplify the expression by canceling out common factors:
1/(1−x2)1/(1-x^2)1/(1−x2) + (x2+x+1)/(x3+1)(x^2 + x + 1)/(x^3 + 1)(x2+x+1)/(x3+1)
Therefore, the simplified form of the expression is:
1/1−x21-x^21−x2 + x2+x+1x^2 + x + 1x2+x+1/x3+1x^3 + 1x3+1