化简无理指数幂.主要是思路啊大侠们遇到这种题如何插手啊化简（-查字典问答网

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　　化简无理指数幂.主要是思路啊大侠们遇到这种题如何插手啊化简（X+Y)/(X^(1/3)+Y^(1/3))-(X^(4/3)-Y^(4/3))/(X^(2/3)-Y^(2/3))咋做啊

　　化简无理指数幂.主要是思路啊大侠们遇到这种题如何插手啊

　　化简（X+Y)/(X^(1/3)+Y^(1/3))-(X^(4/3)-Y^(4/3))/(X^(2/3)-Y^(2/3))咋做啊

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2020-03-1719:56

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邱忠义

　　第一个乘X^(1/3)-Y^(1/3)就行了--

　　(X+Y)/(X^(1/3)+Y^(1/3))-(X^(4/3)-Y^(4/3))/(X^(2/3)-Y^(2/3))

　　=(X+Y)(X^(1/3)-Y^(1/3))/(X^(1/3)+Y^(1/3))(X^(1/3)-Y^(1/3))-(X^(4/3)-Y^(4/3))/(X^(2/3)-Y^(2/3))

　　=(X+Y)(X^(1/3)-Y^(1/3))/(X^(2/3)-Y^(2/3))-(X^(4/3)-Y^(4/3))/(X^(2/3)-Y^(2/3))

　　=[(X+Y)(X^(1/3)-Y^(1/3))-(X^(4/3)-Y^(4/3))]/(X^(2/3)-Y^(2/3))

　　=[(X^(4/3)-XY^(1/3)+X^(1/3)Y-Y^(4/3)-X^(4/3)+Y^(4/3)]/(X^(2/3)-Y^(2/3))

　　=(X^(1/3)Y-XY^(1/3))/(X^(2/3)-Y^(2/3))

　　=(X^(1/3)Y-XY^(1/3))(X^(4/3)+X^(2/3)Y^(2/3)+Y^(4/3))/(X^(2/3)-Y^(2/3))(X^(4/3)+X^(2/3)Y^(2/3)+Y^(4/3))

　　=(X^(1/3)Y-XY^(1/3))(X^(4/3)+X^(2/3)Y^(2/3)+Y^(4/3))/(X^2-Y^2)

　　=(X^(5/3)Y+XY^(5/3)+X^(1/3)Y^(7/3)-X^(7/3)Y^(1/3)-X^(5/3)Y-XY^(5/3))/(X^2-Y^2)

2020-03-17 20:00:40

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