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
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)