\(\frac{a+5}{a-5}=\frac{b+6}{b-6}\Rightarrow\left(a+5\right)\left(b-6\right)=\left(a-5\right)\left(b+6\right)\Rightarrow a.b+5.b-6a-30=a.b-5.b+6.a-30\Rightarrow a.b+10.b=a.b+12a\)\(\Rightarrow10.b=12.a\Rightarrow5.b=6.a\Rightarrow\frac{a}{b}=\frac{5}{6}\left(đpcm\right)\)
\(\frac{a+5}{a-5}=\frac{b+6}{b-6}\Leftrightarrow\left(a+5\right)\left(b-6\right)=\left(a-5\right)\left(b+6\right)\)
=> 6a = 5b
=> \(\frac{a}{b}=\frac{5}{6}\)
\(\frac{a+5}{a-5}=\frac{b+6}{b-6}\)
=> (a + 5)(b - 6) = (b + 6)(a - 5)
=> ab + 5b - 6a - 30 = ab + 6a - 5b - 30
=> 10b = 12a
=> \(\frac{a}{b}=\frac{10}{12}=\frac{5}{6}\)(đpcm)
