Question

Cho a + 5/ a - 5 = b + 6/b - 6 (a không bằng 5; b không bằng 6). Chứng minh rằng a/b = 5/6

 

Answer 1

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

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

=> ab - 6a + 5b - 30 = ab + 6a - 5b - 30

=> -6a + 5b = 6a - 5b

=> 10b = 12a

=> 5b = 6a

=> \(\frac{a}{b}=\frac{5}{6}\)(đpcm)

Answer 2

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

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

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

<=> \(\frac{10}{a-5}=\frac{12}{b-6}\)

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

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

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

<=> 5b = 6a

<=> 5/6 = a/b ( đpcm )