Ta có: \(\frac{a+5}{a-5}=\frac{b+6}{b-6}=>\frac{a+5}{b+6}=\frac{a-5}{b-6}\)
Áp dụng tính chất của dãy tỉ số bằng nhau ta có:
\(\frac{a+5}{b+6}=\frac{a-5}{b-6}=\frac{a+5+a-5}{b+6+b-6}=\frac{2a}{2b}=\frac{a}{b}=\frac{a+5-\left(a-5\right)}{b+6-\left(b-6\right)}=\frac{5+5}{6+6}=\frac{10}{12}=\frac{5}{6}\)
Vậy \(\frac{a}{b}=\frac{5}{6}\)
Vì \(\frac{a+5}{a-5}=\frac{b+6}{b-6}\Rightarrow\left(a+5\right)\left(b-6\right)=\left(a-5\right)\left(b+6\right)\)
\(\Rightarrow ab-6a+5b-30=ab+6a-5b-30\)
\(\Rightarrow ab+5b+5b=ab+6a+6a\)
\(\Rightarrow10b=12a\)
\(\Rightarrow a=\frac{b.10}{12}=b.\frac{5}{6}\)
\(\Rightarrow\frac{a}{b}=\frac{6}{5}\)
