Question

Cho a+b+c=2015 và 1/(a+b) +1/(b+c)+1/(c+a)=1/90

Tính S=a/(b+c)+b/(c+a)+(c/(b+a)

Answer 1

\(S=\frac{a}{b+c}+\frac{b}{c+a}+\frac{c}{b+a}=\frac{a+b+c}{b+c}+\frac{a+b+c}{c+a}+\frac{a+b+c}{a+b}-3=\left(a+b+c\right)\left(\frac{1}{b+c}+\frac{1}{c+a}+\frac{1}{a+b}\right)-3=2015.\frac{1}{90}-3=19\frac{7}{18}\)