Question

已知x>0,y<0,z>0,且x的绝对值小于y的绝对值，y的绝对值大于z的绝对值，化简x加z的绝对值加y加z的绝对值减

x加y的绝对值

Answer 1

已知x>0,y<0,z>0,且︱x︱<︱y︱，︱y︱>︱z︱，化简︱x+z︱+︱y+z︱-︱x+y︱
解：∵x>0，z>0，∴x+z>0；故︱x+z︱=x+z；
∵y<0，z>0，且︱y︱>︱z︱，∴y+z<0；故︱y+z︱=-(y+z)；
∵x>0，y<0，且︱x︱<︱y︱，∴x+y<0；故︱x+y︱=-(x+y)
于是得：︱x+z︱+︱y+z︱-︱x+y︱=(x+z)-(y+z)-[-(x+y)]=x+z-y-z+x+y=2x

Answer 2

x加z的绝对值加y加z的绝对值减x加y的绝对值
=(x+z)-(y+z)-(x+y)
=x+z-y-z-x-y
=-2y

Answer 3

!x+z!+!y+z!-!x+y!
=(x+z)-(z-y)+(y-x)
=x+z-z+y+y-x
=2y