Question

[Nguyễn Trung Hiếu]

Cho tỉ lệ thức: \(\dfrac{a}{b}=\dfrac{c}{d}\left(a,b,c,d\ne0\right)\)

 Chứng minh:

1) \(\dfrac{a+b}{b}=\dfrac{c+d}{d}\)

2) \(\dfrac{5a+3b}{5a-3b}=\dfrac{5c+3d}{5c-3d}\)

Answer 1

[Nguyễn Đức Trí]

a) \(\dfrac{a}{b}=\dfrac{c}{d}\left(a;b;c;d\ne0\right)\)

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

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

\(\Rightarrow dpcm\)

b) \(\dfrac{a}{b}=\dfrac{c}{d}\)

\(\Rightarrow\dfrac{a}{c}=\dfrac{b}{d}\)

\(\Rightarrow\dfrac{5a}{5c}=\dfrac{3b}{3d}=\dfrac{5a+3b}{5c+3d}=\dfrac{5a-3b}{5c-3d}\)

\(\Rightarrow\dfrac{5a+3b}{5a-3b}=\dfrac{5c+3d}{5c-3d}\)

\(\Rightarrow dpcm\)

Answer 2

[Nguyễn Trung Hiếu]

Thanks