Question

cho \(\frac{a+5}{a-5}=\frac{b+6}{b-6}\)(a khác 5 , b khác 6) Chứng minh \(\frac{a}{b}=\frac{5}{6}\)

Answer 1

\(\frac{a+5}{a-5}=\frac{b+6}{b-6}\) => (a + 5)(b - 6) = (a - 5)(b + 6) => ab - 6a + 5b - 30 = ab + 6a - 5b - 30 

=>\(-6a+5b\) = 6a - 5b =\(-\left(6a-5b\right)\)  => 6a - 5b = 0 => 6a = 5b => \(\frac{a}{b}=\frac{5}{6}\)(đpcm)

Answer 2

\(\frac{a+5}{a-5}=\frac{b+6}{b-6}\Rightarrow\frac{a+5}{b+6}=\frac{a-5}{b-6}=\frac{2a}{2b}=\frac{a}{b}\)

Suy ra:\(\frac{a+5}{b+6}=\frac{a}{b}\Rightarrow a.\left(b+6\right)=b.\left(a+5\right)\)

=>ab+6a=ab+5b

=>6a=5b

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

Answer 3

Phan Thanh Tịnh lớp 7 có lẽ ko có khả năng làm như vậy