Question

已知|a|=|c|,化简|a-b|-|a+b|+|a+c|+|c-b|

Answer 1

|a|=|c|,则a=c或者a=-c

当a=c时

|a-b|-|a+b|+|a+c|+|c-b|

=|a-b|-|a+b|+|a+a|+|a-b|

=2|a-b|-|a+b|+2|a|

当a=-c时c=-a

|a-b|-|a+b|+|a+c|+|c-b|

=|a-b|-|a+b|+|a-a|+|-a-b|

=|a-b|-|a+b|+0+|a-b|

=|a-b|