1、15.2.2分式的加减知能演练提升一、能力提升1.化简4xx2-4-xx-2的结果是()A.-x2+2xB.-x2+6xC.-xx+2D.xx-22.化简1x-3-x+1x2-1(x-3)的结果是()A.2B.2x-1C.2x-3D.x-4x-13.化简2x-12x2-1+1x+1的结果是()A.2B.2x+1C.2x-1D.-24.化简1-1m+1(m+1)的结果是.5.已知ab=-1,a+b=2,则式子ba+ab的值是.6.已知1a+1b=5(ab),求ab(a-b)-ba(a-b)的值.7.先化简,再求值:m-m2-1m2+2m+1m-1m,其中m满足:m2-m-1=0.8.请利用1m-
2、3,mm+3和3m2-9这三个分式组成一个算式,来表示其中两个分式的商减去第三个分式的差,并化简.二、创新应用9.阅读理解题:若1-3xx2-1=Mx+1+Nx-1,试求M,N的值.解:等式右边通分,得M(x-1)+N(x+1)(x+1)(x-1)=(M+N)x+N-Mx2-1,根据题意,得M+N=-3,N-M=1,解得M=-2,N=-1.仿照上题解法解答下题:已知5x-4(x-1)(2x-1)=Ax-1+B2x-1,试求A,B的值.知能演练提升一、能力提升1.C原式=4x(x-2)(x+2)-x(x+2)(x-2)(x+2)=4x-x2-2x(x+2)(x-2)=-xx+2,故选C.2.B1
3、x-3-x+1x2-1(x-3)=x2-1-x2+2x+3(x-3)(x+1)(x-1)(x-3)=2(x+1)(x-3)(x-3)(x+1)(x-1)=2x-1.3.A2x-12x2-1+1x+1=2x-12(x+1)(x-1)+x-1(x+1)(x-1)=2x-11x-1=2.故选A.4.m1-1m+1(m+1)=m+1-(m+1)1m+1=m+1-1=m.5.-6ba+ab=b2+a2ab=(a+b)2-2abab.ab=-1,a+b=2,ba+ab=-6.6.解原式=a2ab(a-b)-b2ab(a-b)=(a+b)(a-b)ab(a-b)=a+bab=1b+1a=5.7.解m-m2-1m2+2m+1m-1m=m-(m+1)(m-1)(m+1)2mm-1=m-mm+1=m2m+1.当m2-m-1=0时,m2=m+1,故原式=m2m+1=1.8.解答案不唯一,如3m2-9mm+3-1m-3=3(m+3)(m-3)m+3m-1m-3=3m(m-3)-1m-3=3-mm(m-3)=-1m.二、创新应用9.解等式右边通分,得Ax-1+B2x-1=A(2x-1)+B(x-1)(x-1)(2x-1)=(2A+B)x-(A+B)(x-1)(2x-1).根据题意,得2A+B=5,A+B=4,解得A=1,B=3.
