\(\frac{a+5}{a-5}=\frac{b+6}{b-6}\\ \Rightarrow\left(a+5\right)\left(b-6\right)=\left(b+6\right)\left(a-5\right) \\ \Leftrightarrow ab-6a+5b-30=ab-5b+6a-30\\ \Leftrightarrow12a=10b\\ \Leftrightarrow\frac{a}{10}=\frac{b}{12}=\frac{a}{b}=\frac{10}{12}=\frac{5}{6}\)
Vậy \(\frac{a}{b}=\frac{5}{6}\)
\(\frac{a+5}{a-5}=\frac{b+6}{b-6}\left(a\ne5;b\ne6\right).\)
\(\Rightarrow\left(a+5\right).\left(b-6\right)=\left(a-5\right).\left(b+6\right)\)
\(\Rightarrow ab-6a+5b-30=ab+6a-5b-30\)
\(\Rightarrow ab-6a+5b=ab+6a-5b\)
\(\Rightarrow-6a+5b=6a-5b\)
\(\Rightarrow-6a-6a=-5b-5b\)
\(\Rightarrow-12a=-10b\)
\(\Rightarrow12a=10b\)
\(\Rightarrow\frac{a}{b}=\frac{10}{12}\)
\(\Rightarrow\frac{a}{b}=\frac{5}{6}.\)
Vậy \(\frac{a}{b}=\frac{5}{6}.\)
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