Question

[Nguyễn Hữu Lực 2]

1. Cho a/b=c/d .Chứng tỏ rằng : 

a. a/b=a+c/b+d 

b, a+b/c+d=a/c

Answer 1

[Vuacua1s]

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

Ta có : \(\frac{ad}{bd}+\frac{bc}{bd}=\frac{ad+bc}{bd+bd}=\frac{a+c}{b+d}\)

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

Answer 2

[Nguyễn Phương Uyên]

\(a,\)đặt \(\frac{a}{b}=\frac{c}{d}=k\left(1\right)\)

\(\frac{a}{b}=k\Rightarrow a=b.k\)

\(\frac{c}{d}=k\Rightarrow c=d.k\)

\(\Rightarrow\frac{a+c}{b+d}=\frac{b.k+d.k}{b+d}=\frac{k\left(b+d\right)}{b+d}=k\left(2\right)\)

\(\left(1\right)\left(2\right)\Rightarrow\frac{a}{b}=\frac{c}{d}=\frac{a+c}{b+d}\left(đpcm\right)\)