Question

cho ti le thuc \(\frac{a}{b}=\frac{c}{d}\)chung minh:

\(\frac{5a+2c}{5b+2d}=\frac{a-4c}{b-4d}\)

Answer 1

\(\frac{a}{b}=\frac{c}{d}\Leftrightarrow\frac{a}{c}=\frac{b}{d}\)

Theo TCDTSBN:

\(\frac{a}{c}=\frac{b}{d}=\frac{a+b}{c+d}=\frac{a-b}{c-d}\Leftrightarrow\frac{a+b}{a-b}=\frac{c+d}{c-d}\left(đpcm\right)\)

Answer 2

Áp dụng TCDTSBN ta có:

\(\frac{a}{b}=\frac{c}{d}=\frac{5a}{5b}=\frac{2c}{2d}=\frac{4c}{4d}=\frac{5a+2c}{5b+2d}=\frac{a-4c}{b-4d}\)

k nhé!