已知x<0,xy<0.化简| x-y-1 | + | y-x+3 |
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已知x<0,xy<0.化简| x-y-1 | + | y-x+3 |
![已知x<0,xy<0.化简| x-y-1 | + | y-x+3 |](/uploads/image/z/20107291-67-1.jpg?t=%E5%B7%B2%E7%9F%A5x%EF%BC%9C0%2Cxy%EF%BC%9C0.%E5%8C%96%E7%AE%80%7C+x-y-1+%7C+%2B+%7C+y-x%2B3+%7C)
∵XY<0
∴X,Y异号
∵X<0
∴Y>0
∴X-Y-1<0,Y-X+3>0
∴|X-Y-1|+|Y-X+3|
=-(X-Y-1)+(Y-X+3)
=-X+Y+1+Y-X+3
=2Y-2X+4
∴X,Y异号
∵X<0
∴Y>0
∴X-Y-1<0,Y-X+3>0
∴|X-Y-1|+|Y-X+3|
=-(X-Y-1)+(Y-X+3)
=-X+Y+1+Y-X+3
=2Y-2X+4
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