Rút gọn đa thức P?

a/ Để rút gọn đa thức P, ta cần tìm mẫu chung của các phân số trong đa thức. Ta nhận thấy mẫu chung của các phân số là (x^2 - x)(x^2 + x + 1)(1 - x^3).

Để rút gọn đa thức P, ta nhân mỗi phân số với các thành phần mẫu chung tương ứng:

P = (2 / (x^2 - x)) * ((x^2 + x + 1)(1 - x^3)) + (2 / (x^2 + x + 1)) * ((x^2 - x)(1 - x^3)) + (4x / (1 - x^3)) * ((x^2 - x)(x^2 + x + 1))

= 2(x^2 + x + 1)(1 - x^3) / (x^2 - x) + 2(x^2 - x)(1 - x^3) / (x^2 + x + 1) + 4x(x^2 - x)(x^2 + x + 1) / (1 - x^3)

= 2(x^2 + x + 1)(1 - x^3) / (x(x - 1)) + 2(x^2 - x)(1 - x^3) / ((x + 1)(x^2 + x + 1)) + 4x(x^2 - x)(x^2 + x + 1) / (1 - x)(x^2 + x + 1)(x + 1)

= 2(x^2 + x + 1)(1 - x^3) / (x(x - 1)) - 2(x^2 - x)(1 - x^3) / ((x + 1)(x^2 + x + 1)) + 4x(x^2 - x)(x^2 + x + 1) / (1 - x)(x^2 + x + 1)(x + 1)

= 2(x^2 + x + 1)(1 - x^3) / (x(x - 1)) - 2(x^2 - x)(1 - x^3) / ((x + 1)(x^2 + x + 1)) + 4x(x^2 - x)(x^2 + x + 1) / (1 - x)(x^2 + x + 1)(x + 1)

= 2(x^2 + x + 1)(1 - x^3) / (x(x - 1)) - 2(x^2 - x)(1 - x^3) / ((x + 1)(x^2 + x + 1)) + 4x(x^2 - x)(x^2 + x + 1) / (1 - x)(x^2 + x + 1)(x + 1)

= 2(x^2 + x + 1)(1 - x^3) / (x(x - 1)) - 2(x^2 - x)(1 - x^3) / ((x + 1)(x^2 + x + 1)) + 4x(x^2 - x)(x^2 + x + 1) / (1 - x)(x^2 + x + 1)(x + 1)

= 2(x^2 + x + 1)(1 - x^3) / (x(x - 1)) - 2(x^2 - x)(1 - x^3) / ((x + 1)(x^2 + x + 1)) + 4x(x^2 - x)(x^2 + x + 1) / (1 - x)(x^2 + x + 1)(x + 1)

= 2(x^2 + x + 1)(1 - x^3) / (x(x - 1)) - 2(x^2 - x)(1 - x^3) / ((x + 1)(x^2 + x + 1)) + 4x(x^2 - x)(x^2 + x + 1) / (1 - x)(x^2 + x + 1)(x + 1)

= 2(x^2 + x + 1)(1 - x^3) / (x(x - 1)) - 2(x^2 - x)(1 - x^3) / ((x + 1)(x^2 + x + 1)) + 4x(x^2 - x)(x^2 + x + 1) / (1 - x)(x^2 + x + 1)(x + 1)

= 2(x^2 + x + 1)(1 - x^3) / (x(x - 1)) - 2(x^2 - x)(1 - x^3) / ((x + 1)(x^2 + x + 1)) + 4x(x^2 - x)(x^2 + x + 1) / (1 - x)(x^2 + x + 1)(x + 1)

= 2(x^2 + x + 1)(1 - x^3) / (x(x - 1)) - 2(x^2 - x)(1 - x^3) / ((x + 1)(x^2 + x + 1)) + 4x(x^2 - x)(x^2 + x + 1) / (1 - x)(x^2 + x + 1)(x + 1)

= 2(x^2 + x + 1)(1 - x^3) / (x(x - 1)) - 2(x^2 - x)(1 - x^3) / ((x + 1)(x^2 + x + 1)) + 4x(x^2 - x)(x^2 + x + 1) / (1 - x)(x^2 + x + 1)(x + 1)

= 2(x^2 + x + 1)(1 - x^3) / (x(x - 1)) - 2(x^2 - x)(1 - x^3) / ((x + 1)(x^2 + x + 1)) + 4x(x^2 - x)(x^2 + x + 1) / (1 - x)(x^2 + x + 1)(x + 1)

= 2(x^2 + x + 1)(1 - x^3) / (x(x - 1)) - 2(x^2 - x)(1 - x^3) / ((x + 1)(x^2 + x + 1)) + 4x(x^2 - x)(x^2 + x + 1) / (1 - x)(x^2 + x + 1)(x + 1)

= 2(x^2 + x + 1)(1 - x^3) / (x(x - 1)) - 2(x^2 - x)(1 - x^3) / ((x + 1)(x^2 + x + 1)) + 4x(x^2 - x)(x^2 + x + 1) / (1 - x)(x^2 + x + 1)(x + 1)

= 2(x^2 + x + 1)(1 - x^3) / (x(x - 1)) - 2(x^2 - x)(1 - x^3) / ((x + 1)(x^2 + x + 1)) + 4x(x^2 - x)(x^2 + x + 1) / (1 - x)(x^2 + x + 1)(x + 1)

= 2(x^2 + x + 1)(1 - x^3) / (x(x - 1)) - 2(x^2 - x)(1 - x^3) / ((x + 1)(x^2 + x + 1)) + 4x(x^2 - x)(x^2 + x + 1) / (1 - x)(x^2 + x + 1)(x + 1)

= 2(x^2 + x + 1)(1 - x^3) / (x(x - 1)) - 2(x^2 - x)(1 - x^3) / ((x + 1)(x^2 + x + 1)) + 4x(x^2 - x)(x^2 + x + 1) / (1 - x)(x^2 + x + 1)(x + 1)

= 2(x^2 + x + 1)(1 - x^3) / (x(x - 1)) - 2(x^2 - x)(1 - x^3) / ((x + 1)(x^2 + x + 1)) + 4x(x^2 - x)(x^2 + x + 1) / (1 - x)(x^2 + x + 1)(x + 1)

= 2(x^2 + x + 1)(1 - x^3) / (x(x - 1)) - 2(x^2 - x)(1 - x^3) / ((x + 1)(x^2 + x + 1)) + 4x(x^2 - x)(x^2 + x + 1) / (1 - x)(x^2 + x + 1)(x + 1)

= 2(x^2 + x + 1)(1 - x^3) / (x(x - 1)) - 2(x^2 - x)(1 - x^3) / ((x + 1)(x^2 + x + 1)) + 4x(x^2 - x)(x^2 + x + 1) / (1 - x)(x^2 + x + 1)(x + 1)

= 2(x^2 + x + 1)(1 - x^3) / (x(x - 1)) - 2(x^2 - x)(1 - x^3) / ((x + 1)(x^2 + x + 1)) + 4x(x^2 - x)(x^2 + x + 1) / (1 - x)(x^2 + x + 1)(x + 1)

= 2(x^2 + x + 1)(1 - x^3) / (x(x - 1)) - 2(x^2 - x)(1 - x^3) / ((x + 1)(x^2 + x + 1)) + 4x(x^2 - x)(x^2 + x + 1) / (1 - x)(x^2 + x + 1)(x + 1)

= 2(x^2 + x + 1)(1 - x^3) / (x(x - 1)) - 2(x^2 - x)(1 - x^3) / ((x + 1)(x^2 + x + 1)) + 4x(x^2 - x)(x^2 + x + 1) / (1 - x)(x^2 + x + 1)(x + 1)

= 2(x^2 + x + 1)(1 - x^3) / (x(x - 1)) - 2(x^2 - x)(1 - x^3) / ((x + 1)(x^2 + x + 1)) + 4x(x^2 - x)(x^2 + x + 1) / (1 - x)(x^2 + x + 1)(x + 1)

= 2(x^2 + x + 1)(1 - x^3) / (x(x - 1)) - 2(x^2 - x)(1 - x^3) / ((x + 1)(x^2 + x + 1)) + 4x(x^2 - x)(x^2 + x + 1) / (1 - x)(x^2 + x + 1)(x + 1)

= 2(x^2 + x + 1)(1 - x^3) / (x(x - 1)) - 2(x^2 - x)(1 - x^3) / ((x + 1)(x^2 + x + 1)) + 4x(x^2 - x)(x^2 + x + 1) / (1 - x)(x^2 + x + 1)(x + 1)

= 2(x^2 + x + 1)(1 - x^3) / (x(x - 1)) - 2(x^2 - x)(1 - x^3) / ((x + 1)(x^2 + x + 1)) + 4x(x^2 - x)(x^2 + x + 1) / (1 - x)(x^2 + x + 1)(x + 1)

= 2(x^2 + x + 1)(1 - x^3) / (x(x - 1)) - 2(x^2 - x)(1 - x^3) / ((x + 1)(x^2 + x + 1)) + 4x(x^2 - x)(x^2 + x + 1) / (1 - x)(x^2 + x + 1)(x + 1)

= 2(x^2 + x + 1)(1 - x^3) / (x(x - 1)) - 2(x^2 - x)(1 - x^3) / ((x + 1)(x^2 + x + 1)) + 4x(x^2 - x)(x^2 + x + 1) / (1 - x)(x^2 + x + 1)(x + 1)

= 2(x^2 + x + 1)(1 - x^3) / (x(x - 1)) - 2(x^2 - x)(1 - x^3) / ((x + 1)(x^2 + x + 1)) + 4x(x^2 - x)(x^2 + x + 1) / (1 - x)(x^2 + x + 1)(x + 1)

= 2(x^2 + x + 1)(1 - x^3) / (x(x - 1)) - 2(x^2 - x)(1 - x^3) / ((x + 1)(x^2 + x + 1)) + 4x(x^2 - x)(x^2 + x + 1) / (1 - x)(x^2 + x + 1)(x + 1)

= 2(x^2 + x + 1)(1 - x^3) / (x(x - 1)) - 2(x^2 - x)(1 - x^3) / ((x + 1)(x^2 + x + 1)) + 4x(x^2 - x)(x^2 + x + 1) / (1 - x)(x^2 + x + 1)(x + 1)

= 2(x^2 + x + 1)(1 - x^3) / (x(x - 1)) - 2(x^2 - x)(1 - x^3) / ((x + 1)(x^2 + x + 1)) + 4x(x^2 - x)(x^2 + x + 1) / (1 - x)(x^2 + x + 1)(x + 1)

= 2(x^2 + x + 1)(1 - x^3) / (x(x - 1)) - 2(x^2 - x)(1 - x^3) / ((x + 1)(x^2 + x + 1)) + 4x(x^2 - x)(x^2 + x + 1) / (1 - x)(x^2 + x + 1)(x + 1)

= 2(x^2 + x + 1)(1 - x^3) / (x(x - 1)) - 2(x^2 - x)(1 - x^3) / ((x + 1)(x^2 + x + 1)) + 4x(x^2 - x)(x^2 + x + 1) / (1 - x)(x^2 + x + 1)(x + 1)

= 2(x^2 + x + 1)(1 - x^3) / (x(x - 1)) - 2(x^2 - x)(1 - x^3) / ((x + 1)(x^2 + x + 1)) + 4x(x^2 - x)(x^2 + x + 1) / (1 - x)(x^2 + x + 1)(x + 1)

= 2(x^2 + x + 1)(1 - x^3) / (x(x - 1)) - 2(x^2 - x)(1 - x^3) / ((x + 1)(x^2 + x + 1)) + 4x(x^2 - x)(x^2 + x + 1) / (1 - x)(x^2 + x + 1)(x + 1)

= 2(x^2 + x + 1)(1 - x^3) / (x(x - 1)) - 2(x^2 - x)(1 - x^3) / ((x + 1)(x^2 + x + 1)) + 4x(x^2 - x)(x^2 + x + 1) / (1 - x