Question

Cho a+5/a-5=b+6/b-6 (a khac 5 b khac 6).Chung minh rang a/b=5/6

Answer 1

\(\frac{a+5}{a-5}=\frac{b+6}{b-6}\)

\(=\frac{a+5}{b+6}=\frac{a-5}{b-6}=\frac{a+5-a+5}{b+6-b+6}=\frac{10}{12}=\frac{5}{6}\)

\(\Rightarrow\frac{a+5}{a-5}=\frac{5}{6}\)

\(\Rightarrow6a+30=5a-25\)

\(\Rightarrow6a-5a=-25-30\)

\(\Rightarrow a=-55\)

\(\Rightarrow\frac{b+6}{b-6}=\frac{5}{6}\)

\(\Rightarrow6b+36=5b-30\)

\(\Rightarrow6b-5b=-30-36\)

\(\Rightarrow b=-66\)

\(\Rightarrow\frac{a}{b}=\frac{-55}{-66}=\frac{5}{6}\left(đpcm\right)\)

Answer 2

Ta co a+5/a-5=b+6/b-6

<=> (a+5).(b-6)=(a-5).(b+6)

<=> 6a=5b

<=> a/b=5/6

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