Question

Cho tỉ lệ thức a/b=c/d
Chứng tỏ rằng

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

Answer 1

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

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

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

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

\(\Rightarrow\)\(\frac{a}{b}-1=\frac{c}{d}-1_{ }\)

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

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

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

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

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

\(d.\)Tương tự \(c\) nhé bn. Chúc bn học tốt!