试说明代数式[(x-y)^2-(x+y)(x-y)]除(-2y)+y的值与y的值无关

题目

试说明代数式[(x-y)^2-(x+y)(x-y)]除(-2y)+y的值与y的值无关

答案

[(x-y)²-(x+y)(x-y)]除(-2y)+y
=[x²-2xy+y²-(x²-y²)]/(-2y)+y
=(-2xy+2y²)/(-2y)+y
=x-y+y
=x
所以代数式与y的值无关
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