北师大版初中数学八年级第五章第二节分式的运算练习题

完成时间：_______ 分钟 得分：_______

一、分式的乘除运算（共6题）

1. 计算：$\frac{3a^2b}{4c} \cdot \frac{8c^2}{9ab^2}$

解：

________________________________________________________________

________________________________________________________________

2. 计算：$\frac{x^2 - 4}{x^2 - 2x} \div \frac{x+2}{x}$

解：

________________________________________________________________

________________________________________________________________

3. 计算：$\frac{2m-6}{m^2-9} \cdot \frac{m+3}{4}$

解：

________________________________________________________________

________________________________________________________________

4. 计算：$\frac{a^2 - b^2}{ab} \div (a-b)$

解：

________________________________________________________________

________________________________________________________________

5. 计算：$\left( -\frac{2x}{y} \right)^2 \cdot \left( \frac{y^2}{4x} \right)^3$

解：

________________________________________________________________

________________________________________________________________

6. 计算：$\frac{x^2 - 5x + 6}{x^2 - 1} \div \frac{x-2}{x^2 + x}$

解：

________________________________________________________________

________________________________________________________________

二、同分母分式的加减运算（共6题）

7. 计算：$\frac{3}{x+1} + \frac{2}{x+1}$

解：

________________________________________________________________

8. 计算：$\frac{5a}{a-b} - \frac{3b}{a-b}$

解：

________________________________________________________________

9. 计算：$\frac{m+2n}{m-n} - \frac{m-n}{m-n}$

解：

________________________________________________________________

10. 计算：$\frac{x^2}{x-3} - \frac{6x-9}{x-3}$

解：

________________________________________________________________

________________________________________________________________

11. 计算：$\frac{2}{y-2} + \frac{y}{y-2} - \frac{y+2}{y-2}$

解：

________________________________________________________________

________________________________________________________________

12. 计算：$\frac{a^2 + 2a + 1}{a+1} - \frac{a^2 - 1}{a+1}$

解：

________________________________________________________________

________________________________________________________________

三、异分母分式的加减运算（共8题）

13. 计算：$\frac{1}{a} + \frac{1}{b}$

解：

________________________________________________________________

________________________________________________________________

14. 计算：$\frac{3}{x} - \frac{2}{x+1}$

解：

________________________________________________________________

________________________________________________________________

15. 计算：$\frac{2}{m-3} + \frac{1}{m+3}$

解：

________________________________________________________________

________________________________________________________________

16. 计算：$\frac{x}{x-y} - \frac{y}{x+y}$

解：

________________________________________________________________

________________________________________________________________

17. 计算：$\frac{1}{a-2} - \frac{4}{a^2-4}$

解：

________________________________________________________________

________________________________________________________________

18. 计算：$\frac{2}{x^2-9} + \frac{1}{x+3}$

解：

________________________________________________________________

________________________________________________________________

19. 计算：$\frac{a+1}{a-1} - \frac{a-1}{a+1}$

解：

________________________________________________________________

________________________________________________________________

20. 计算：$\frac{3}{x-2} - \frac{x}{x+2} + \frac{4}{x^2-4}$

解：

________________________________________________________________

________________________________________________________________

________________________________________________________________