已知有理数a,b,c满足a>0,b/a/>/b/,化简/a+b/+/c-a/+/c-b/

问题描述:

已知有理数a,b,c满足a>0,b/a/>/b/,化简/a+b/+/c-a/+/c-b/

a>0,b|b|,则a+b>0
c|a|,则c-a|c|>|b|,则c-b原式=a+b+a-c+b-c=2a+2b-2c=2(a+b-c)

a>0,b|a|>|b|
|a+b|+|c-a|+|c-b|=(a+b)+(a-c)+(b-c)=2(a+b-c)

a>0,b/a/>/b/
|c|=-c
|a|=a
|b|=-b
-c>a>-b
所以
a+b>0
c-ac-b∴
/a+b/+/c-a/+/c-b/
=a+b -(c-a)-(c-b)
=a+b-c+a-c+b
=2a+2b-2c

2(a+b-c)