y/(x+y)-x/(x-y)=?怎么算?

来源：学生作业帮助网编辑：作业帮时间：2024/06/05 12:28:54

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y/(x+y)-x/(x-y)=?怎么算?
y/(x+y)-x/(x-y)=?怎么算?

y/(x+y)-x/(x-y)=?怎么算?
y/(x+y)-x/(x-y)
=y(x-y)/(x²-y²)-x(x+y)/(x²-y²)
=[y(x-y)-x(x+y)]/(x²-y²)
=(xy-y²-x²-xy)/(x²-y²)
=-(x²+y²)/(x²-y²)

通分后：
分母：(x+y)(x-y)=x^2-y^2
分子：y(x-y)-x(x+y)=xy-y^2-x^2-xy=-(x^2+y^2)
∴原式=-(x^2+y^2)/x^2-y^2

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