Question

Cho a , b , c khác 0 va a+b+c=0

Tính \(M=\frac{a+b}{c}+\frac{b+c}{a}+\frac{a+c}{b}\)

Answer 1

a + b + c = 0  =>  a + b = -c ; b + c = -a ; a + c = -b

Do đó \(M=\frac{-c}{c}+\frac{-a}{a}+\frac{-b}{b}=-1+\left(-1\right)+\left(-1\right)=-3\)

Answer 2

Ta có :\(a+b+c=0=>a+b=-c;b+c=-a;a+c=-b\)

Do đó : \(M=-\frac{c}{c}+-\frac{b}{b}+-\frac{c}{c}=\left(-1\right)+\left(-1\right)+\left(-1\right)=-3\)