早教吧作业答案频道 -->数学-->
已知x/y+z=a,y/z+x=b,z/x+y=c,且x+y+z≠0,则a/1+a+b/1+b+c/1+c的值为
题目详情
已知x/y+z=a,y/z+x=b,z/x+y=c,且x+y+z≠0,则a/1+a+b/1+b+c/1+c的值为
▼优质解答
答案和解析
已知x/(y+z)=a,y/(z+x)=b,z/(x+y)=c,且x+y+z≠0,则a/(1+a)+b/(1+b)+c/(1+c)的值为(建议以后加上括号,以免产生歧义)
1+a=(x+y+z)/(y+z),a/(1+a)=a(y+z)/(x+y+z)=x/(x+y+z)
同理,b/(1+b)=y/(x+y+z)
c/(1+c)=z/(x+y+z)
所以,原题所求
=(x+y+z)/(x+y+z)=1
1+a=(x+y+z)/(y+z),a/(1+a)=a(y+z)/(x+y+z)=x/(x+y+z)
同理,b/(1+b)=y/(x+y+z)
c/(1+c)=z/(x+y+z)
所以,原题所求
=(x+y+z)/(x+y+z)=1
看了 已知x/y+z=a,y/z+...的网友还看了以下：