Question

a) chứng tỏ rằng a/b < c/d ( b>0, d>0) thì a/b < a+c/ b+d <c/d

B. hãy viết 3 số hữu tỉ xen giữa -1/3 va -1/4

Answer 1

Answer 2

a) \(\frac{a}{b}< \frac{c}{d}\Rightarrow ad< bc\)

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

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

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

\(ad< bc\)

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

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

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

\(\Rightarrowđpcm\)

b) \(-\frac{1}{3}=-\frac{16}{48}< -\frac{15}{48};-\frac{14}{48};-\frac{13}{48}< -\frac{12}{48}=-\frac{1}{4}\)