Question

已知x/y+z=a,y/x+z=b,z/x+y=c求a/a+1+b/b+1+c/c+1

Answer 1

x/（y+z）=a, 1/a=(y+z)/x 1/a+1=(x+y+x)/x a/(a+1)=x/(x+y+z)

y/（z+x）=b, 化为b/(b+1)=y/(x+y+z)

z/（x+y）=c 化为c/(c+1)=z/(x+y+z)

三式相加：a/(a+1)+b/(b+1)+c/(c+1)=(x+y+z)/(x+y+z)=1