a) \(\frac{a}{b}=\frac{c}{d}\Rightarrow\frac{a}{b}=\frac{c}{d}=\frac{7a}{7b}=\frac{5c}{5d}\)

\(\Rightarrow\frac{a}{b}=\frac{7a+5c}{7b+5d}\)

Cho ab =cd 

Chứng minh ab =7a+5c7b+5d (7b+5d khác 0)

Đặt a/b=c/d=k => a=bk,c=dk

Ta có: \(\frac{a}{b}=\frac{bk}{b}=k\left(1\right)\)

\(\frac{7a+5c}{7b+5d}=\frac{7bk+5dk}{7b+5d}=\frac{k\left(7b+5d\right)}{7b+5d}=k\left(2\right)\)

Từ (1) vavf (2) => a/b=7a+5c/7b+5d

Cảm ơn bn nhìu nha

\(\dfrac{a}{b}=\dfrac{7a}{7b}\\ \dfrac{c}{d}=\dfrac{5c}{5d}\Rightarrow\dfrac{a}{b}=\dfrac{7a}{7b}=\dfrac{5c}{5d}\Rightarrow\dfrac{7a}{7b}=\dfrac{5c}{5d}\)

Áp dụng tính chất dãy tỉ số bằng nhau ta có:

\(\dfrac{7a}{7b}=\dfrac{5c}{5d}=\dfrac{7a+5c}{7b+5d}\)

Mà \(\dfrac{7a}{7b}=\dfrac{a}{b}\Rightarrow\dfrac{a}{b}=\dfrac{5c}{5d}=\dfrac{7a+5c}{7b+5d}\Leftrightarrow\dfrac{a}{b}=\dfrac{7a+5c}{7b+5d}\)

Vậy \(\dfrac{a}{b}=\dfrac{7a+5c}{7b+5d}\left(đpcm\right)\)

\(\dfrac{a}{b}=\dfrac{c}{d}\)

\(\Rightarrow ad=bc\)

\(\Rightarrow5ad=5bc\)

\(\Rightarrow7ab+5ad=7ab+5bc\)

\(\Rightarrow a\left(7b+5d\right)=b\left(7a+5c\right)\)

\(\Rightarrow\dfrac{a}{b}=\dfrac{7a+5c}{7b+5d}\rightarrowđpcm\)

Lời giải:
Đặt $\frac{a}{b}=\frac{c}{d}=t\Rightarrow a=bt; c=dt$

Ta có:
\(\frac{7a-11c}{7b-11d}=\frac{7bt-11dt}{7b-11d}=\frac{t(7b-11d)}{7b-11d}=t(1)\)

\(\frac{7a+11c}{7b+11d}=\frac{7bt+11dt}{7b+11d}=\frac{t(7b+11d)}{7b+11d}=t(2)\)

Từ $(1);(2)\Rightarrow \frac{7a-11c}{7b-11d}=\frac{7a+11c}{7b+11d}$