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已知x+y=a,2x-y=-2a,求[（x/y-y/x)/(x+y)-x(1/x-1/y)]/[(x+1)/y]的值
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已知x+y=a,2x-y=-2a,求[（x/y-y/x)/(x+y)-x(1/x-1/y)]/[(x+1)/y]的值
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答案和解析
[（x/y-y/x)/(x+y)-x(1/x-1/y)]/[(x+1)/y]
=[(x-y)/xy-1+x/y]/[(x+1)/y]
=[(x-y)(1+x)/xy]/[(x+1)/y]
=(x-y)/x
由x+y=a,2x-y=-2a可解得
x=-a/3 y=4a/3
代入得[（x/y-y/x)/(x+y)-x(1/x-1/y)]/[(x+1)/y]=(x-y)/x=5
=[(x-y)/xy-1+x/y]/[(x+1)/y]
=[(x-y)(1+x)/xy]/[(x+1)/y]
=(x-y)/x
由x+y=a,2x-y=-2a可解得
x=-a/3 y=4a/3
代入得[（x/y-y/x)/(x+y)-x(1/x-1/y)]/[(x+1)/y]=(x-y)/x=5
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