Question

先化简，再求值：【（x²y-4y³）/（x²+4xy+4y²）】*【（4xy）/（x-2y）+x】

其中x=√2 -1，y=√2 +1

Answer 1

原式=y(x+2y)(x-2y)/(x+2y)²*(4xy+x²-2xy)/(x-2y)
=y(x-2y)/(x+2y)*x(x+2y)/(x-2y)
=xy
=（√2-1）（√2+1）
=2-1
=1

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Answer 2

原式=[y(x²-4y²)/(x+2y)²]*[4xy/(x-2y)+x]
=[y(x+2y)(x-2y)/(x+2y)²]*[4xy+x(x-2y)]/(x-2y)
=[y(x-2y)/(x+2y)]*[(x²+2xy)/(x-2y)]
=[y(x-2y)/(x+2y)]*[x(x+2y)/(x-2y)]
=xy
=(√2-1)(√2+1)
=2-1
=1

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