课时训练(三) 分式(限时:20分钟)|夯实基础|1.[2022·莱芜]若x,y的值均扩大为原来的3倍,则下列分式的值保持不变的是( )A.2+xx-yB.2yx2C.2y33x2D.2y2(x-y)22.[2022·天津]计算2x+3x+1-2xx+1的结果为( )A.1B.3C.3x+1D.x+3x+13.[2022·淄博]若分式|x|-1x+1的值为零,则x的值是( )A.1B.-1C.±1D.24.[2022·北京]如果a2+2a-1=0,那么代数式a-4a·a2a-2的值是( )A.-3B.-1C.1D.35.[2022·内江]已知:1a-1b=13,则abb-a的值是( )5\nA.13B.-13C.3D.-36.[2022·苏州]计算1+1x÷x2+2x+1x的结果是( )A.x+1B.1x+1C.xx+1D.x+1x7.[2022·盐城]要使分式1x-2有意义,则x的取值范围是 . 8.[2022·沈阳]化简:2aa2-4-1a-2= . 9.[2022·永州]化简:1+1x-1÷x2+xx2-2x+1= . 10.[2022·绥化]当x=2时,代数式2x+1x+x÷x+1x的值是 . 11.a,b互为倒数,代数式a2+2ab+b2a+b÷1a+1b的值为 . 12.化简:(1)[2022·泸州]1+2a-1÷a2+2a+1a-1;(2)[2022·十堰]1a-1-1a2+a÷a2-1a2+2a+1.5\n13.[2022·盐城]先化简,再求值:1-1x+1÷xx2-1,其中x=2+1.|拓展提升|14.[2022·烟台]先化简,再求值:1+x2+2x-2÷x+1x2-4x+4,其中x满足x2-2x-5=0.5\n参考答案1.D [解析]根据分式的基本性质,2(3y)2(3x-3y)2=18y29(x-y)2=2y2(x-y)2,故答案为D.2.C [解析]2x+3x+1-2xx+1=2x+3-2xx+1=3x+1,故选C.3.A [解析]分式的值为零,同时满足两个条件:分子等于零、分母不为零,则|x|-1=0且x+1≠0,所以x=1.4.C [解析]原式=a2-4a·a2a-2=(a+2)(a-2)a·a2a-2=a(a+2)=a2+2a,而a2+2a-1=0,∴原式=1.5.C [解析]∵1a-1b=b-aab=13,∴abb-a=3.故选择C.6.B [解析]原式=x+1x×x(x+1)2=1x+1,故选B.7.x≠28.1a+2 [解析]原式=2a(a+2)(a-2)-a+2(a+2)(a-2)=2a-a-2(a+2)(a-2)=a-2(a+2)(a-2)=1a+2.9.x-1x+1 [解析]原式=x-1+1x-1×(x-1)2x(x+1)=x-1x+1.因此,本题填:x-1x+1.10.3 [解析]原式=x2+2x+1x÷x+1x=(x+1)2x×xx+1=x+1.当x=2时,原式=1+2=3.故答案为3.11.1 [解析]原式=a2+2ab+b2a+b÷a+bab=(a+b)·aba+b=ab,∵a,b互为倒数,∴a·b=1,∴原式=1.12.解:(1)原式=a-1+2a-1·a-1(a+1)2=1a+1.(2)原式=1a-1-1a(a+1)×(a+1)2(a+1)(a-1)=1a-1-1a(a-1)=a-1a(a-1)=1a.13.解:原式=x+1-1x+1×x2-1x=xx+1×(x+1)(x-1)x=x-1.当x=2+1时,原式=2+1-1=2.5\n14.解:1+x2+2x-2÷x+1x2-4x+4=x-2+x2+2x-2÷x+1(x-2)2=x(1+x)x-2·(x-2)2x+1=x(x-2)=x2-2x.∵x2-2x-5=0,∴x2-2x=5,∴原式=5.5
