Question

Cho \(a,b,c\in N\) Giải thích tại sao , nếu \(\dfrac{a}{b}< 1\) thì \(\dfrac{a}{b}< \dfrac{a+c}{b+c}\)

Answer 1

\(\dfrac{a}{b}=\dfrac{a\left(b+c\right)}{b\left(b+c\right)}=\dfrac{ab}{b\left(b+c\right)}+\dfrac{ac}{b\left(b+c\right)};\dfrac{a+c}{b+c}=\dfrac{b\left(a+c\right)}{b\left(b+c\right)}=\dfrac{ab}{b\left(b+c\right)}+\dfrac{bc}{b\left(b+c\right)}\)

Theo đề bài \(\dfrac{a}{b}< 1\) suy ra \(a< b\) nên \(ac< bc\). Do đó \(\dfrac{ac}{b\left(b+c\right)}< \dfrac{bc}{b\left(b+c\right)}\)

Suy ra \(\dfrac{a}{b}< \dfrac{a+c}{b+c}\)