Question

1/(1-x)-2/(x^2+x+1)=(2x+1)/(1-x^3) пж срочно

Answer 1

1/(1-x)-2/(x²+x+1)=(2x+1)/(1-x³)       ОДЗ: 1-x³≠0    x³≠1     x≠1.
(x²+x+1-2*(1-x))/((1-x)*(x²+x+1)=(2x+1)/(1-x³)
(x²+x+1-2+2x)/(1-x)³=(2x+1)/(1-x³)
x²+3x-1=2x+1
x²+x-2=0   D=9
x₁=-2      x₂=1   ∉ОДЗ
Ответ: x=-2.

Answer 2

To solve the given equation:

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

We can start by simplifying the left-hand side of the equation by finding a common denominator:

[(x^2 + x + 1) - 2(1 - x)] / [(1-x)(x^2 + x + 1)] = (2x + 1)/(1 - x^3)

Simplifying the numerator and denominator:

(x^2 + x + 3) / [(1-x)(x^2 + x + 1)] = (2x + 1)/(1 - x^3)

Multiplying both sides by (1 - x^3) and simplifying:

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

Expanding both sides:

x^5 - x^4 - 2x^3 + 2x^2 + 4x + 3 = 0

This equation can be solved numerically, but it is difficult to find exact solutions. Therefore, we can conclude that the solution to the given equation is the set of all values of x that satisfy the fifth-degree polynomial equation:

x^5 - x^4 - 2x^3 + 2x^2 + 4x + 3 = 0