Ta có:\(\frac{a}{b}\)=\(\frac{a.\left(b+c\right)}{b.\left(b+c\right)}=\frac{a.b+ac}{b.\left(b+c\right)}\)

\(\frac{a+c}{b+c}=\frac{\left(a+c\right).b}{\left(b+c\right).b}=\frac{a.b+b.c}{b.\left(b+c\right)}\)

Vì \(\frac{a}{b}\)<1 =>a<b

=>a.c<b.c

=>a.b+a.c<a.b+b.c