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化简求值:x?yx+2y÷x2?y2x2+4xy+4y2%2,其中x=1+2...

原式=x?yx+2y?(x+2y)2(x+y)(x?y)-2=x+2yx+y-2=x+2y?2(x+y)x+y=-xx+y,当x=1+2,y=1-2时,原式=-1+22.

x?yx+2y÷x2?y2x2+4xy+4y2-1=x?yx+2y×(x+2y)2(x?y)(x+y)?1=x+2yx+y?1=yx+y故答案为:yx+y

原式=x?yx+2y×(x+2y)2(x?y)(x+y)-2=-xx+y;当x=2-2,y=22-1时,原式=-2?22?2+22?1=4-32.

x?yx?2y÷x2?y2x2?4xy+4y2=x?yx?2y?(x?2y)2(x+y)(x?y)=x?2yx+y;当x=1+2,y=1-2时,原式=1+2?2(1?2)1+2+1?2=3

原式=1-x?yx+2y×(x+2y)2(x+y)(x?y)=1-x+2yx+y=-yx+y.故答案为:-yx+y.

(1)∵x2-4x-1=0,∴x2-4x=1,原式=4x2-12x+9-(x2-y2)-y2=3x2-12x+9=3(x2-4x)+9=3×1+9=12;(2)原式=x+2yx+y?xyx+2y÷x+yxy=x+2yx+y?xyx+2y?xyx+y=x2y2(x+y)2当x=-2,y=3时,原式=36.

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