已知x\(y+z)=a,y\(x+z)=b,z\(x+y)=c,试求a\(a+1)+b\(b+1)+c\(c+1)的值（写过程）

Question

已知x\(y+z)=a,y\(x+z)=b,z\(x+y)=c,试求a\(a+1)+b\(b+1)+c\(c+1)的值（写过程）

Answer 1

x\(y+z)=a,a+1=x/(y+z)=(x+y+z)/(x+z)
所以a/(a+1)=x/(x+y+z)
y\(x+z)=b,同理可得b/(b+1)=y/(x+y+z)
z\(x+y)=c,同理可得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