Question

[phandangnhatminh]

cho tỉ lệ thức \(\frac{a+b}{c+d}=\frac{a-2b}{c-2d}\left(b,d\ne0\right)\)

chứng minh \(\frac{a}{b}=\frac{c}{d}\)

Answer 1

[nguyenthitulinh]

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

=> \(\left(a+b\right)\left(c-2d\right)=\left(c+d\right)\left(a-2b\right)\)

=> ac - 2ab + bc - 2bd = ac - 2bc + ad - 2bd

=>  -3ad = -3bc

=>  ad = bc 

=>   \(\frac{a}{b}=\frac{c}{d}\left(đpcm\right)\)