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 .
