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

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

Áp dụng TC DTSBN ta có :

\(\frac{a+5}{b+6}=\frac{a-5}{b-6}=\frac{\left(a+5\right)+\left(a-5\right)}{\left(b+c\right)+\left(b-6\right)}=\frac{2a}{2b}=\frac{a}{b}\) (1)

\(\frac{a+5}{b+6}=\frac{a-5}{b-6}=\frac{\left(a+5\right)-\left(a-5\right)}{\left(b+6\right)-\left(b-6\right)}=\frac{10}{12}=\frac{5}{6}\)(2)

Từ (1) ; (2) \(\Rightarrow\frac{a}{b}=\frac{5}{6}\)(đpcm)