M=\(\dfrac{b+c}{a}\)+\(\dfrac{c+a}{b}\)+\(\dfrac{a+b}{c}\)
M+3=\(\dfrac{b+c}{a}\)+1+\(\dfrac{c+a}{b}\)+1+\(\dfrac{a+b}{c}\)+1
M+3=\(\dfrac{b+c+a}{a}\)+\(\dfrac{c+a+b}{b}\)+\(\dfrac{a+b+c}{c}\)
M+3= (a+b+c)(\(\dfrac{1}{a}\)+\(\dfrac{1}{b}\)+\(\dfrac{1}{c}\))= (a+b+c).0=0
=>M=0-3=-3