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2.分式的基本性质1.下列运算正确的是(D)(A)y-x-y=-yx-y (B)2x+y3x+y=23(C)x2+y2x+y=x+y(D)y-xx2-y2=-1x+y2.下列分式中是最简分式的是(A)(A)2xx2+1 (B)42x(C)x-1x2-1 (D)1-xx-13.若将分式4x2x-3y中的x,y都扩大到原来的3倍,则分式的值(A)(A)不变 (B)扩大3倍(C)扩大6倍 (D)缩小到原来的134.(整体求解思想)(xx新乡一中月考)若y2-7y+12=0,则分式13yy2-20y+12的值是(B)(A)1 (B)-1 (C)13 (D)-135.若ab=2,bc=6,则ac=12.6.若梯形的面积是(x+y)2(x0,y0),上底是2x(x0),下底是2y(y0),高是z(z0),则z=x+y.7.化简:x2-2xy+y2-1x-y-1=x-y+1.8.(辅助未知数法)若x2=y3=z40,则2x+3yz=134.9.不改变分式的符号,使分式2-3x33-b3的分子、分母最高次项的系数为 正数.解:2-3x33-b3=-(3x3-2)-(b3-3)=3x3-2b3-3.10.通分:(1)12x3y2z,14x2y3,16xy4;(2)1x2-y2,1x2+xy.解:(1)12x3y2z,14x2y3,16xy4的最简公分母为12x3y4z,所以12x3y2z=16y22x3y2z6y2=6y212x3y4z,14x2y3=13xyz4x2y33xyz=3xyz12x3y4z,16xy4=12x2z6xy42x2z=2x2z12x3y4z.(2)1x2-y2,1x2+xy的最简公分母为x(x-y)(x+y),所以1x2-y2=1(x-y)(x+y)=xx(x-y)(x+y),1x2+xy=1x(x+y)=x-yx(x-y)(x+y).11.(拓展探究)不改变分式的值,把分式35x+3100.6x-0.5中分子、分母的各项系数化为整数,然后选择一个你喜欢的整数代入求值.解:35x+3100.6x-0.5=(35x+310)10(0.6x-0.5)10=6x+36x-5.因为6x-50,所以x56.所以当x=0时,原式=60+360-5=-35.12.(一题多解)已知xy=3,求x2+2xy-3y2x2-xy+y2的值.解:法一分子、分母的每一项除以y2,得x2+2xy-3y2x2-xy+y2=(xy)2+2xy-3(xy)2-xy+1=9+6-39-3+1=127.法二已知xy=3,得x=3y,代入得x2+2xy-3y2x2-xy+y2=(3y)2+23yy-3y2(3y)2-3yy+y2=9y2+6y2-3y29y2-3y2+y2=12y27y2=127.
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