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第2课时分式的混合运算1.化简:(1x-3-x+1x2-1)(x-3)的结果是(B)(A)2(B)2x-1(C)2x-3(D)x-4x-12.计算:(1+1a-1)(1+1a2-1)的结果是(C)(A)1(B)a+1(C)a+1a(D)1a-13.当x=6,y=3时,代数式(xx+y+2yx+y)3xyx+2y的值是(C)(A)2 (B)3 (C)6(D)94.化简(y-1x)(x-1y)的结果是(D)(A)-yx (B)-xy (C)xy(D)yx5.若x=-1,则3x-6x2-4x+2x2+4x+4-2+x的值是0.6.化简:a+2a2-1a-1a2+4a+41a+2+2a2-1=1a-1.7.(整体求解法)若x+1x=2,则(x2+2+1x2)(x2-1x2)(x-1x)+2 019的值 是2 027.8.化简:(2a+1+a+2a2-1)aa-1.解:(2a+1+a+2a2-1)aa-1=2(a-1)+a+2(a+1)(a-1)a-1a=3a(a+1)(a-1)a-1a=3a+1.9.先化简:x2x+3x2-9x2-2x+xx-2,再在-3,-1,0,2,2中选择一个合适的x值代入求值.解:x2x+3x2-9x2-2x+xx-2=x2x+3(x+3)(x-3)x(x-2)+xx-2=x(x-3)x-2+xx-2=x2-3x+xx-2=x(x-2)x-2=x,为使原分式有意义x-3,0,2,所以x只能取-1或2.当x=-1时,原式=-1.或当x=2时,原式=2.(选择其中一个即可)10.(分类讨论题)若a的立方等于它的本身,求(aa+2+2a-2)1a2-4a3a2+4 的值.解:原式=a(a-2)+2(a+2)(a+2)(a-2)1a2-4a3a2+4=a2+4(a+2)(a-2)(a+2)(a-2)a3a2+4=a3.因为a的立方等于它的本身,所以a=0或1或-1.所以当a=0时,原式=03=0;当a=1时,原式=13=1;当a=-1时,原式=(-1)3=-1.所以(aa+2+2a-2)1a2-4a3a2+4的值是0或1或-1.11.(拓展题)(xx德州)先化简,再求值:x-3x2-1x-3x2+2x+1-(1x-1+1),其中x是不等式组5x-33(x+1),12x-13(x+1),12x-19-32x的解集是3x3(x+1),12x-19-32x的整数解是x=4.所以当x=4时,原式=14-1=13.
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