初二数学分式的加减法试题与答案1

绝密★启用前

分式的加减法 测试时间:20分钟

一、选择题 1、计算a+3a

-3a 的结果是( )

A.

a+6a

B.

a -6a

C.1

a D.1

2.计算

x 2

x -1-

1

x -1

的结果是( )

A.x 2

-1 B.x-1 C.x+1 D.1 3、化简x -2x -1+2x -11-x

的结果是( ) A.-x+3x -1

B.-

x+1x -1

C.-x-1

D.3

4.下列计算正确的是( ) A.2

m +1

-m =3

m B.a

a -

b -b

b -a =1 C.

2

y+2-

1+y 2+y =1+y

y+2 D.a

(a -b )

2

-

b

(b -a )

2

=

1

a -b

5、化简

x 2+2xy+y 2

x 2-y 2

-y x -y

的结果是( )

A.x

x+y B.y

x+y C.x

x -y D.y

x -y

二、填空题

6、若(x-y-2)2

+|xy+3|=0,则(

3x

x -y

+

2x y -x

)÷1

y 的值是 . 7.已知2x -3x+1=2+m

x+1,则m= . 8.若a b =5

3,则

a 2a 2-

b 2

+

4ab -2b 2b 2-a 2

+

2ab -b 2a 2-b 2

的值为 .

三、解答题

9.小明用电脑录入汉字文稿的速度是他手抄汉字文稿速度的4倍,若小明手抄汉字文稿的速度为m 字/小时,那么他用电脑录入4 000字文稿比手抄文稿少用多少小时? 10.阅读下面的计算过程:

x -3x 2-1-2-2x 1-x 2=x -3x 2-1-2x -2x 2-1

①

=x-3-2x+2② =-x-1.③

(1)上面计算过程中从哪一步开始出现错误?请写出该步骤的序号: ; (2)错误原因是 ; (3)写出正确的计算过程.

参考答案 一、选择题

1.答案 D

a+3a

-3a

=

a+3-3a

=1.故选D.

2.答案 C 原式=x 2-1x -1=(x+1)(x -1)

x -1

=x+1.

3.答案 B 原式=

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

x -1,故选B.

4.答案 D A.2

m +1

-m =2

m -1

m =2-1m

=1m ,错误;B.a a -b -b b -a =a a -b +b a -b =a+b a -b ,错误;C.2y+2-1+y 2+y =

2-(1+y )y+2

=1-y

y+2,错

误;D.

a

(a -b )

2

-

b

(b -a )

2

=

a -b

(a -b )

2

=1

a -

b ,正确.故选D.

5.答案 C 原式=(x+y )2

(x+y )(x -y )-y

x -y =x+y

x -y -y

x -y =x x -y , 故选C.

二、填空题

6.答案 -3

2

解析 原式=(3x x -y -2x x -y )÷1

y =x

x -y ·y

=

xy

x -y

,

∵(x -y-2)2

+|xy+3|=0, ∴x -y=2,xy=-3, ∴原式=-3

2=-3

2. 7.答案 -5 解析 ∵

2x -3x+1=2+

m

x+1

=

2x+2+m x+1

,∴-3=2+m,解得m=-5.

8.答案 1

4 解析

a 2a 2-

b 2

+4ab -2b 2b 2-a 2

+2ab -b 2a 2-b 2

=a 2

a 2-

b 2-4ab -2b 2a 2-b 2

+2ab -b 2a 2-b 2=a 2-4ab+2b 2+2ab -b 2

a 2-

b 2

=(a -b )

2

(a+b )(a -b )=a -b

a+b .

∵a b =5

3,∴设a=5k,b=3k(k≠0),∴原式=a -b a+b =5k -3k 5k+3k =1

4.

三、解答题

横线以内不许答题

9.解析 由题意得

4 000m

-

4 0004m

=

4 000m

-

1 000m

=

3 000m

(小时).

答:他用电脑录入4 000字文稿比手抄文稿少用3 000m

小时.

10.解析 (1)②. (2)丢了分母. (3)x -3x 2-1-2-2x 1-x 2=x -3x 2-1-2x -2x 2-1=x -3-(2x -2)x 2-1

=

x -3-2x+2

x 2-1

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

1-x .