Question

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

a ) \(\frac{a+c}{c}=\frac{b+d}{d}\)

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

c ) \(\frac{a^2+c^2}{b^2+d^2}=\frac{ab}{bd}\)

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Answer 1

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

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

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

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

Answer 2

Ta có :

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

\(\Leftrightarrow\frac{3a}{3c}=\frac{5b}{5d}=\frac{3a+5b}{3c+5d}=\frac{3a-5b}{3c-5d}\)

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