Question

cmr a/b<c/d(b,d>0)thì a/b<a+c/b+d<c/d

Answer 1

Giải:
Ta có: \(\frac{a}{b}< \frac{c}{d}\) (1)

\(\Rightarrow ad< bc\)

+) \(ad+ab< bc+ab\)

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

\(\Rightarrow\frac{a}{b}< \frac{a+c}{b+d}\) (2)

+) \(ad+cd< bc+cd\)

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

\(\Rightarrow\frac{c}{d}>\frac{a+c}{b+d}\) (3)

Từ (1), (2) và (2) suy ra \(\frac{a}{b}< \frac{a+c}{b+d}< \frac{c}{d}\)