Question

已知y+z分之x =a , x+z分之y =b , x+y分之z =c,试求a+1分之a + b+1分之b + c+1分之c 的值

a+1分之a + b+1分之b + c+1分之c 可否化简

Answer 1

(a/a+1)+(b/b+1)+(c/c+1)
=[1/1+(1/a)] +[1/1+(1/b)]+[1/1+(1/c)]

代入得
1/(x+y+z/x)+1/(x+y+z/y)+1/(x+y+z/z)
=(x+y+z)/(x+y+z)=1

追问

为何a/a+1=1/1+(1/a)

Answer 2

a/a+1 + b/b+1 + c/c+1 = 3-1/a+1 -1/b+1 -1/c+1
a+1=(a+y+z)/(y+z) 1/a+1=(y+z) /a+y+z
1/b+1 =x+z/a+y+z 1/c+1 =x+y/a+y+z
代入得 3-2=1