Question

[Đoàn Thị Hương Giang]

Mn giúp tớ với. Toán 7: 

Answer 1

[HT.Phong (9A5)]

Ta có:

\(x< y\)

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

\(\Rightarrow ad< cb\)

Cộng 2 vế cho ab

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

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

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

\(\Rightarrow x< \dfrac{a+b}{b+d}\left(1\right)\)

\(y>x\)

\(\Rightarrow\dfrac{c}{d}>\dfrac{a}{b}\)

\(\Rightarrow cb>ad\)

Cộng 2 vế cho cd:

\(\Rightarrow cb+cd>ad+cd\)

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

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

\(\Rightarrow y>\dfrac{a+b}{b+d}\left(2\right)\)

Từ (1) và (2) 

\(\Rightarrow x< \dfrac{a+c}{b+d}< y\left(dpcm\right)\)