Question

Cho 2 phân số : \(\frac{a}{b}=\frac{c}{d}\)

Chứng minh rằng : \(\frac{a+b}{b}=\frac{c+d}{d}\)

Answer 1

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

                              \(\Rightarrow ad+bd=bc+bd\)

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

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

Answer 2

Đặt a/b = c/d = k => a = bk ; c = dk

\(\Rightarrow\hept{\begin{cases}\frac{bk+b}{b}=\frac{b\left(k+1\right)}{b}=k+1\left(1\right)\\\frac{dk+d}{d}=\frac{d\left(k+1\right)}{d}=k+1\left(2\right)\end{cases}}\)

Từ (1) và (2) => đpcm

Answer 3

ta có: \(\frac{a}{b}=\frac{c}{d}\Rightarrow\frac{a}{c}=\frac{b}{d}\)

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

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