华师大版八年级下册1. 分式的乘除一课一练

这是一份华师大版八年级下册1. 分式的乘除一课一练，共6页。试卷主要包含了2　分式的运算，【易错题】计算，计算等内容，欢迎下载使用。

第1课时 分式的乘除
基础过关全练
知识点1 分式的乘法
1.计算x-y2x-1·yx-y的结果是( )

A.xy2x-1 B.x2x-1
C.y2x-1 D.(x-y)2(2x-1)y
2.(2023山东济南长清期中)计算m2-n2m·2mm+n的结果是( )
A.2(m-n)2B.2(m2-n2)
C.2(m-n)D.2(m+n)
3.【易错题】(2023甘肃兰州一模)计算:1a+1·(-a2-a)=( )
A.a B.-a C.a+1 D.aa+1
4.(1)计算:6xy5z2·10z39y= ;
(2)化简:2x+4x-2·x2+2xx2+4x+4= .
5.计算:
(1)-m2n3x·-6xy5mn2;(2)x2+1x-6·x2-36x3+x;
(3)a2-1ab·2aba2+2a+1;(4)(a-2)·a2-4a2-4a+4.
6.【新独家原创】先化简,再求值:a2-1a2-2a+1·2aa2+a,其中a的值是4的算术平方根.
知识点2 分式的除法
7.化简x2yab2÷xy3ab的结果是( )
A.3ya B.3xabC.3yab D.3xb
8.(2023河北保定高碑店模拟)分式4xx2-1÷xx-1的值可能等于( )
A.0 B.1 C.2 D.4
9.(2023云南昆明西山二模)计算:aa-1÷aa2-2a+1= .
10.(2023广东汕头潮南二模)把式子x-1x-3÷x2-1x2-6x+9化到最简,其结果为 .
11.计算:
(1)a2xyb2z÷a2yz2b2x;
(2)a-2a+3÷a2-4a2+6a+9;
(3)x2-y24x2+12xy÷x-yx+3y;
(4)(xy-x2)÷x-yxy;
(5)x3-2x2+4xx2-4x+4÷x2-2x+4x-2.
知识点3 分式的乘方
12.计算2b2-3a32的结果是( )
A.4b49a5B.2b49a5C.4b49a6D.4b43a6
13.(2023河北中考)化简x3y3x2的结果是( )
A.xy6B.xy5C.x2y5D.x2y6
14.(2022福建华安一中月考)计算-b22a2·6b4的结果是 .
15.计算:
(1)2x3y2·3y4x3;
(2)15x5(-2y)3÷-3x8y2.
知识点4 分式的乘除混合运算
16.(2023北京怀柔期末)计算81-a2a2+6a+9÷a-92a+6·a+3a+9的结果为( )
A.12B.1C.-1D.-2
17.计算:
(1)2x5x-3÷325x2-9·x5x+3;
(2)2x-6x2-4x+4÷3-x4x2-16·x-2x+22;
(3)(x2-4y2)÷2y+xxy·1x(2y-x);
(4)x2-4x+2÷(x-2)·1x-2;
(5)a2-4a2+2a-8÷(a2-4)·a2-4a+4a-2;
(6)x2-1x2-4x+4÷(x+1)·x2-3x+2x-1.
答案全解全析
1.C x-y2x-1·yx-y=y2x-1.故选C.
2.C m2-n2m·2mm+n=(m+n)(m-n)m·2mm+n=2(m-n),故选C.
3.B 解题时易出现符号错误.原式=-1a+1·(a2+a)=-1a+1·a(a+1)=-a.故选B.
4.答案 (1)4xz3;(2)2xx-2
解析 (1)原式=60xyz345yz2=4xz3.
(2)原式=2(x+2)x-2·x(x+2)(x+2)2=2xx-2.
5.解析 (1)原式=2my5n.
(2)原式=x2+1x-6·(x+6)(x-6)x(x2+1)=x+6x.
(3)原式=(a+1)(a-1)ab·2ab(a+1)2=2a-2a+1.
(4)原式=(a-2)·(a+2)(a-2)(a-2)2=a+2.
6.解析 a2-1a2-2a+1·2aa2+a=(a+1)(a-1)(a-1)2·2aa(a+1)=2a-1.
∵a的值是4的算术平方根,∴a=2.
当a=2时,原式=22-1=2.
7.D x2yab2÷xy3ab=x2yab2·3abxy=3xb,故选D.
8.B 4xx2-1÷xx-1=4x(x+1)(x-1)·x-1x=4x+1,4x+1≠0,故选项A不符合题意;当x=3时,4x+1=1,且原式有意义,故选项B符合题意;当x=1时,4x+1=2,但此时原式无意义,故选项C不符合题意;当x=0时,4x+1=4,但此时原式无意义,故选项D不符合题意.故选B.
9.答案 a-1
解析 原式=aa-1·(a-1)2a=a-1.
10.答案 x-3x+1
解析 x-1x-3÷x2-1x2-6x+9=x-1x-3÷(x-1)(x+1)(x-3)2=x-1x-3·(x-3)2(x-1)(x+1)=x-3x+1.
11.解析 (1)原式=a2xyb2z·2b2xa2yz=2x2z2.
(2)原式=a-2a+3·(a+3)2(a+2)(a-2)=a+3a+2.
(3)原式=(x+y)(x-y)4x(x+3y)·x+3yx-y=x+y4x.
(4)原式=-x(x-y)·xyx-y=-x2y.
(5)原式=x(x2-2x+4)(x-2)2·x-2x2-2x+4=xx-2.
12.C 2b2-3a32=4b49a6,故选C.
13.A x3y3x2=x3·y6x2=xy6,故选A.
14.答案 32a2
解析 原式=b44a2·6b4=64a2=32a2.
15.解析 (1)2x3y2·3y4x3=4x29y2·27y364x3=3y16x.
(2)原式=15x5-8y3·64y29x2=-40x33y.
16.D 81-a2a2+6a+9÷a-92a+6·a+3a+9=-(a+9)(a-9)(a+3)2·2(a+3)a-9·a+3a+9=-2.故选D.
17.解析 (1)原式=2x5x-3·(5x+3)(5x-3)3·x5x+3=23x2.
(2)原式=2(x-3)(x-2)2·4(x+2)(x-2)-(x-3)·(x-2)2(x+2)2
=-8(x+2)x-2·(x-2)2(x+2)2=-8(x-2)x+2=16-8xx+2.
(3)原式=(x+2y)(x-2y)·xyx+2y·-1x(x-2y)=-y.
(4)原式=(x-2)(x+2)x+2·1x-2·1x-2=1x-2.
(5)原式=(a+2)(a-2)(a+4)(a-2)·1(a+2)(a-2)·(a-2)2a-2=1a+4.
(6)原式=(x+1)(x-1)(x-2)2·1x+1·(x-1)(x-2)x-1=x-1x-2.