Question

Cho \(\frac{a+5}{a-5}=\frac{b+6}{b-6}\left(a\ne5;b\ne6\right).\)Chứng minh rằng \(\frac{a}{b}=\frac{5}{6}\)

 

Answer 1

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

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

<=> \(1+\frac{10}{a-5}=1+\frac{12}{b-6}\)

<=> \(\frac{10}{a-5}=\frac{12}{b-6}\)

<=> 10( b - 6 ) = 12( a - 5 )

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

<=> 5b - 30 = 6a - 30

<=> 5b = 6a

<=> \(\frac{6}{5}=\frac{b}{a}\)hay \(\frac{a}{b}=\frac{5}{6}\)( đpcm )