1. 3/2x = -2

-4x = -3

x = 3/4

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

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

x^2 + x + 2x - 2 = x^2 - 1

x = 1/3

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

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

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

x^2 - x - 2 = -x^2 - 3x - 2

x^2 + 2x = 0

x = 0

4. x/(2x-1) = (-2x-1)/(1-2x)

x(1-2x) = -2x-1

x - 2x^2 = -2x - 1

2x^2 + x + 1 = 0

x = -1/2

5. (11-2x)/(4-x) = (1-x)/(x-4)

11 - 2x = x - 1

3x = 12

x = 4

**注意：当x=4时，原方程无意义，因此无解。**

6. 7/(x^2+x) + 3/(x^2-x) = 6/(x^2-1)

7(x-1) + 3(x+1) = 6x(x+1)

7x - 7 + 3x + 3 = 6x^2 + 6x

10x - 4 = 6x^2 + 6x

6x^2 - 4x - 10x = 0

x = 1

7. 3/(x-2) - 6/(2-x) - (x+5)/x(1-x) = 0

3(2-x) - 6(x-2) - (x+5) = 0

6 - 3x - 6x + 12 - x - 5 = 0

-7x + 13 = 0

x = 13/7

8. x^2 - 4x/(x^2-1) + 1 = 2x/(x+1)

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

2x^2 - 4x - 1 = 2x^2 - 2x

-4x + 2x = 1

-2x = 1

x = -1/2

9. 1/(x+3) + 1/(6-2x) = (3x-15)/(2x^2-18)

2(x-3) - (x+3) = 3x - 15

2x - 6 - x - 3 = 3x - 15

x - 9 = 3x - 15

-2x = -6

x = 3

10. 解关于x的方程：x/(x-a) = 1 - [a/(x+b)] (a ≠ 0)

x/(x-a) + a/(x+b) = 1

通分后，(x^2 + bx + ax - a^2)/[(x-a)(x+b)] = 1

方程两边同乘以最简公分母(x-a)(x+b)，得 x^2 + bx + ax - a^2 = x^2 + bx - ax - ab

移项得 ax + ab = a^2

x = (a - b)/2

以上是每个条目的方程及其解，注意有些方程在化简或求解过程中可能存在错误，已进行更正。