Question

chứng tỏ rằng nếu \(\dfrac{a}{b}\)<\(\dfrac{c}{d}\)(b > 0, d > 0) thì \(\dfrac{a}{b}\)<\(\dfrac{a+c}{b+d}\)

Answer 1

Ta có: \(\dfrac{a}{b}< \dfrac{c}{d}\Rightarrow ad< bc\)

\(\Rightarrow ad+ab< bc+ab\)

\(\Rightarrow a\left(b+d\right)< b\left(a+c\right)\)

\(\Rightarrow\dfrac{a}{b}< \dfrac{a+c}{b+d}\)

\(\Rightarrowđpcm\)

Answer 2

Vì \(\dfrac{a}{b}< \dfrac{c}{d}\) nên \(ad< bc\)

\(\Rightarrow ad+ab< bc+ab\)

\(\Rightarrow a\left(b+d\right)< b\left(a+c\right)\)

\(\Rightarrow\dfrac{a}{b}< \dfrac{a+c}{b+d}\) (đpcm)

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