先化简,再求值:【(x²y-4y³)/(x²+4xy+4y²)】*【(4xy)/(x-2y)+x】其中x=√2 -1,y=√2 +1
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![先化简,再求值:【(x²y-4y³)/(x²+4xy+4y²)】*【(4xy)/(x-2y)+x】其中x=√2 -1,y=√2 +1](/uploads/image/z/2754300-12-0.jpg?t=%E5%85%88%E5%8C%96%E7%AE%80%2C%E5%86%8D%E6%B1%82%E5%80%BC%EF%BC%9A%E3%80%90%EF%BC%88x%26%23178%3By-4y%26%23179%3B%EF%BC%89%2F%EF%BC%88x%26%23178%3B%2B4xy%2B4y%26%23178%3B%EF%BC%89%E3%80%91%2A%E3%80%90%EF%BC%884xy%EF%BC%89%2F%EF%BC%88x-2y%EF%BC%89%2Bx%E3%80%91%E5%85%B6%E4%B8%ADx%3D%E2%88%9A2+-1%2Cy%3D%E2%88%9A2+%2B1)
先化简,再求值:【(x²y-4y³)/(x²+4xy+4y²)】*【(4xy)/(x-2y)+x】其中x=√2 -1,y=√2 +1
先化简,再求值:【(x²y-4y³)/(x²+4xy+4y²)】*【(4xy)/(x-2y)+x】
其中x=√2 -1,y=√2 +1
先化简,再求值:【(x²y-4y³)/(x²+4xy+4y²)】*【(4xy)/(x-2y)+x】其中x=√2 -1,y=√2 +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
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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