Доведіть тотожність a + a ^ 2 + (2a ^ 2 + 3a + 1)/(a ^ 2 - 1) - (a ^ 3 + 2a)/(a - 1) = - 1 СРОЧНО ДАМ 90 БАЛІВ!! ​

To solve the equation a + a^2 + (2a^2 + 3a + 1)/(a^2 - 1) - (a^3 + 2a)/(a - 1) = -1, you can follow these steps:

1. First, combine like terms and simplify the expression on the left-hand side of the equation:

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

2. Factor the denominators:

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

3. Find a common denominator for the fractions:

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

4. Multiply both sides of the equation by the common denominator to eliminate fractions:

[(a + 1)(a - 1)][a] + [(a + 1)(a - 1)][a^2] + (2a^2 + 3a + 1)(a + 1) - [(a + 1)(a - 1)][(a^3 + 2a)] = -1[(a + 1)(a - 1)]

5. Expand and simplify the equation:

a(a^2 - 1) + a^2(a^2 - 1) + (2a^2 + 3a + 1)(a + 1) - (a^4 - a)(a + 1) = -1

6. Continue simplifying:

a^3 - a + a^4 - a^2 + 2a^2 + 3a + 1 - (a^5 - a^2 + a^4 - a) = -1

7. Combine like terms:

4a^4 - 2a^3 + 3a + 1 - a^5 = -1

8. Move all terms to one side of the equation:

4a^4 - 2a^3 + 3a + 1 - a^5 + 1 = 0

9. Simplify further:

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

10. Factor out a common term 'a' to make it easier to factor:

a(4a^3 - 2a^2 - a^4 + 3) = 0

11. Now, set each factor equal to zero:

a = 0

4a^3 - 2a^2 - a^4 + 3 = 0

You can solve the second equation for 'a' or use numerical methods to find its solutions, as it's a cubic equation.

The solutions to the original equation are a = 0 and the roots of the second equation.