1、第3课时分式知能优化训练一、中考回顾1.(2021天津中考)计算3aa-b-3ba-b的结果是()A.3B.3a+3bC.1D.6aa-b答案:A2.(2020山东威海中考)分式2a+2a2-1-a+11-a化简后的结果为()A.a+1a-1B.a+3a-1C.-aa-1D.-a2+3a2-1答案:B3.(2020内蒙古呼和浩特中考)分式2xx-2与8x2-2x的最简公分母是,方程2xx-2-8x2-2x=1的解是.答案:x(x-2)x=-44.(2020湖南益阳中考)先化简,再求值:(2a-1a+1-aa+1)a-1a,其中a=-2.解:2a-1a+1-aa+1a-1a=a-1a+1a-1a
2、=a-1a+1aa-1=aa+1.当a=-2时,原式=-2-2+1=2.5.(2021四川成都中考)先化简,再求值:1+2a+1a2+6a+9a+1,其中a=3-3.解:1+2a+1a2+6a+9a+1=a+3a+1a+1(a+3)2=1a+3.当a=3-3时,原式=13-3+3=33.二、模拟预测1.使分式x-2(x-1)(x-2)有意义,x应满足的条件是()A.x1B.x2C.x1或x2D.x1,且x2答案:D2.化简m2m-4+164-m的结果是()A.m-4B.m+4C.m+4m-4D.m-4m+4答案:B3.化简a+3a-4a-31-1a-2的结果等于()A.a-2B.a+2C.a-
3、2a-3D.a-3a-2答案:B4.若ab=2,则a2-ab+b2a2+b2的值等于()A.45B.1C.35D.2答案:C5.若代数式2x-1-1的值为零,则x=.答案:36.若x+y=1,且x0,则x+2xy+y2xx+yx的值为.答案:17.化简并求值:1x-y+1x+y2x-yx2-y2,其中x,y满足|x-2|+(2x-y-3)2=0.解:原式=2x(x-y)(x+y)(x-y)(x+y)2x-y=2x2x-y.|x-2|+(2x-y-3)2=0,|x-2|=0,(2x-y-3)2=0.x=2,y=1.原式=2222-1=43.8.先化简,再求值:x2-2xx2-1x-1-2x-1x+1,其中x是不等式组x+30,xx-23+2的整数解.解:原式=x(x-2)(x+1)(x-1)x2-1-2x+1x+1=x(x-2)(x+1)(x-1)x+1x(x-2)=1x-1.解不等式组,得-3x2,则整数解为-2,-1,0,1,2.x2-10,x-20,x0,x1,x2,x0.x=-2.原式=1-2-1=-13.
