To solve the equation, we first need to combine the terms on the left side of the equation:

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

Multiply the first term by (x^2 - 1) and the second term by (x^2 - 2) to get a common denominator:

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

Simplify:

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

Now combine like terms in the numerator:

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

Combine like terms:

(3x^2 - 4) / [(x^2 - 1)(x^2 - 2)] = -2

Now cross multiply:

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

Expand the right side of the equation:

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

Distribute the -2:

3x^2 - 4 = -2x^4 + 6x^2 - 4

Combine like terms on the right side:

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

Rearrange the equation to set it equal to 0:

2x^4 - 3x^2 = 0

Factor out an x^2:

x^2(2x^2 - 3) = 0

This gives us two possible solutions for x^2:

1) x^2 = 0
2) 2x^2 - 3 = 0

For x^2 = 0, we get x = 0.

For 2x^2 - 3 = 0, we get x = √(3/2) or x = -√(3/2)

Therefore, the solutions to the equation are x = 0, x = √(3/2), and x = -√(3/2).