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Question

cho a,b,c,d thuộc Z , b,d>0CMR: nếu $\frac{a}{b}$<$\frac{c}{d}$ thì $\frac{a}{b}$< $\frac{a+c}{b+d}$<$\frac{c}{d}$giúp nhanh tớ tk !

Đinh Đức Hùng · Accepted Answer

$\frac{a}{b}< \frac{c}{d}$$\Rightarrow ad>bc$$\Rightarrow ad+ab< bc+ab$$\Rightarrow a\left(b+d\right)< b\left(a+c\right)$$\Rightarrow\frac{a}{b}< \frac{a+c}{b+d}$ (1)$\Rightarrow ad+cd< bc+cd$$\Leftrightarrow d\left(a+c\right)< c\left(b+d\right)$$\Rightarrow\frac{a+c}{b+d}< \frac{c}{d}$ (2)Từ (1); (2) => $\frac{a}{b}< \frac{a+c}{b+d}< \frac{c}{d}$ (đpcm)Câu trả lời: $\frac{a}{b}< \frac{c}{d}$$\Rightarrow ad>bc$$\Rightarrow ad+ab< bc+ab$$\Rightarrow a\left(b+d\right)< b\left(a+c\right)$$\Rightarrow\frac{a}{b}< \frac{a+c}{b+d}$ (1)$\Rightarrow ad+cd< bc+cd$$\Leftrightarrow d\left(a+c\right)< c\left(b+d\right)$$\Rightarrow\frac{a+c}{b+d}< \frac{c}{d}$ (2)Từ (1); (2) => $\frac{a}{b}< \frac{a+c}{b+d}< \frac{c}{d}$ (đpcm)

Yến Nhi Libra Virgo HotG... · Answer

$\frac{a}{b}< \frac{c}{d}$$\Rightarrow ad=bc$$\Rightarrow ad+ab< bc+ab$$\Rightarrow a\left(b-d\right)< b\left(a+c\right)$$\Rightarrow\frac{a}{b}< \frac{a+c}{b+d}\left(1\right)$$\Rightarrow ad+cd< bc+cd$$\Leftrightarrow d\left(a+c\right)< c\left(b+d\right)$$\Rightarrow\frac{a+c}{b+d}< \frac{c}{d}\left(2\right)$Từ ( 1 ) và ( 2 )$\Rightarrow\frac{a}{b}< \frac{a+c}{b+d}< \frac{c}{d}$( đpcm )Câu trả lời: $\frac{a}{b}< \frac{c}{d}$$\Rightarrow ad=bc$$\Rightarrow ad+ab< bc+ab$$\Rightarrow a\left(b-d\right)< b\left(a+c\right)$$\Rightarrow\frac{a}{b}< \frac{a+c}{b+d}\left(1\right)$$\Rightarrow ad+cd< bc+cd$$\Leftrightarrow d\left(a+c\right)< c\left(b+d\right)$$\Rightarrow\frac{a+c}{b+d}< \frac{c}{d}\left(2\right)$Từ ( 1 ) và ( 2 )$\Rightarrow\frac{a}{b}< \frac{a+c}{b+d}< \frac{c}{d}$( đpcm )

Nhók_Lạnh Lùng · Answer

$\frac{a}{b}< \frac{c}{d}$$\Rightarrow ad=bc$$\Rightarrow ad+ab< bc+ab$$\Rightarrow a\left(b-d\right)< b\left(a+c\right)$$\Rightarrow\frac{a}{b}< \frac{a+c}{b+d}\left(1\right)$$\Rightarrow ad+cd< bc+cd$$\Leftrightarrow d\left(a+c\right)< c\left(b+d\right)$$\Rightarrow\frac{a+c}{b+d}< \frac{c}{d}\left(2\right)$Từ ( 1 ) và ( 2 )$\Rightarrow\frac{a}{b}< \frac{a+c}{b+d}< \frac{c}{d}$( đpcm )Câu trả lời: $\frac{a}{b}< \frac{c}{d}$$\Rightarrow ad=bc$$\Rightarrow ad+ab< bc+ab$$\Rightarrow a\left(b-d\right)< b\left(a+c\right)$$\Rightarrow\frac{a}{b}< \frac{a+c}{b+d}\left(1\right)$$\Rightarrow ad+cd< bc+cd$$\Leftrightarrow d\left(a+c\right)< c\left(b+d\right)$$\Rightarrow\frac{a+c}{b+d}< \frac{c}{d}\left(2\right)$Từ ( 1 ) và ( 2 )$\Rightarrow\frac{a}{b}< \frac{a+c}{b+d}< \frac{c}{d}$( đpcm )

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