若x+y+z不等于0,且x/（y+z）=y/（z+x）=z/（x+y）,求x/（x+y+z）的值大神们帮帮忙

题目

若x+y+z不等于0,且x/（y+z）=y/（z+x）=z/（x+y）,求x/（x+y+z）的值大神们帮帮忙

答案

x/（y+z）=y/（z+x）=z/（x+y）, 所以（x+y+z)/(y+z+z+x+x+y)=x/(y+z) (x+y+z)/(2x+2y+2z)=x/(y+z) 1/2=x/(y+z) y+z=2x x/(x+y+z) =x/(x+2x) =1/3