- 1. 解方程：$\frac{1}{x} = \frac{2}{x + 1}$
- 2. 解方程：$\frac{x}{x - 2} = \frac{3}{x + 1}$
- 3. 解方程：$\frac{2x}{x + 3} = 1$
- 4. 解方程：$\frac{3}{x - 1} + \frac{2}{x + 1} = 1$
- 5. 解方程：$\frac{x^2 - 1}{x - 1} = 0$
- 6. 解方程：$\frac{2}{x} + \frac{1}{x - 1} = 1$
- 7. 解方程：$\frac{1}{x + 2} = \frac{3}{x - 2}$
- 8. 解方程：$\frac{x}{x - 3} + \frac{2}{x + 1} = 1$
- 9. 解方程：$\frac{2x + 1}{x - 1} = 3$
- 10. 解方程：$\frac{1}{x} + \frac{1}{x + 1} = \frac{2}{x(x + 1)}$
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