Question

Cho tỉ lệ thức a/b=c/d. Chứng tỏ b khác (-d) thì (a+c)/(b+d)=a/b

Answer 1

->ad=bc

 ->ad+dc=bc+dc

 ->d(a+c)=c(b+d)

 ->(a+c)/(b+d)=c/d=a/b.ok

Answer 2

\(\frac{a}{b}=\frac{c}{d}\Rightarrow\frac{a}{c}=\frac{b}{d}\) => \(\frac{a}{c}+1=\frac{b}{d}+1\)=> \(\frac{a}{c}+\frac{c}{c}=\frac{b}{d}+\frac{d}{d}\)=> \(\frac{a+c}{c}=\frac{b+d}{d}\) => \(\frac{a+c}{b+d}=\frac{c}{d}=\frac{a}{b}\)

Vậy \(\frac{a+c}{b+d}=\frac{a}{b}\)