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5.4分式的加减(2)—异分母分式的加减(见学生用书P34)
1.化简2mm2一4-1m-2,结果是(C)
A.m-2 B.m+2 C.Im+2 D.Im-2
2.若y=x一y,则分式1x一1y=(C)
A.Ixy B.y-x C.-1 D.I
3.分式1x2一2x与1x的最简公分母是xc一2)
4.若ab=1,a十b=2,则1a十1b的值为2
【解析】1a+1b=b十aab,
当ab=1,a+b=2时,原式=21=2
5.若x=3y,则4x2一y2-x十xy的值是一12
【解析】原式=4y-(x十y)2(x十y)(x一y)=y-x2-2y-y2(x一y)(x十y)=-
(x-y)2(x-y)(x十y=-x-x十y
当x=3y时,原式=一3y-yy+y=-12
6.计算:
(1)y3x2-16y.
(2加-2x2-2x-4在
(3)1-x2x-6+xx-3.(4x十1x-1-4x2-1.
(⑤1x-1+x+1.(6r+1-4x2-1-1
解:(1)原式=2y262y-x62y=2y2-x6r2y
(2)原式=x-2x2-x(2x-4)x2=x-2-2x2+42=-2x2-5x+2x2.
(3)原式=1-x2(x-3)+2x2(x-3)=1-x+2x2(x-3)=1+x2x-6.
(4)原式=(x+1)2(x+1)(x-1)-4(x+1)(x-1)=x2+2x+1-4x(x+1)(x-1)
=(x-1)2(x+1)(x-1)=x-Ix+1.
(5)原式=1x-1+x2-1x-1=1+x2-1x-1=x2x-1.
(6原式=x(-1)(x+1)(x-I)-4(x+1)(-1)-(x+1)(x-1)(x+1)(x-1)
=x2-x-4-x2+1(x+1)(x-1)=-x十3x2-1
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