已知x、y、z均为实数x+y+z不等于0,a=x/y+z,b=y/z+x,c=z/x+y,那么a/a+1+b/b+1+c/2+1的值是?

Question

已知x、y、z均为实数x+y+z不等于0,a=x/y+z,b=y/z+x,c=z/x+y,那么a/a+1 + b/b+1 +c/2+1的值是?

Answer 1

a+1=x+y+z/y+z
a/a+1=x/x+y+z
同理,b/b+1=y/x+y+z
c/c+1=z/x+y+z
所以a/a+1 +b/b+1 +c/c+1 =x+y+z/x+y+z=1