\(\frac{a+5}{a-5}=\frac{b+6}{b-6}\Rightarrow\left(a+5\right)\left(b-6\right)=\left(a-5\right)\left(b+6\right)\Rightarrow a.b+5.b-6a-30=a.b-5.b+6.a-30\Rightarrow a.b+10.b=a.b+12a\)\(\Rightarrow10.b=12.a\Rightarrow5.b=6.a\Rightarrow\frac{a}{b}=\frac{5}{6}\left(đpcm\right)\)
\(\frac{a+5}{a-5}=\frac{b+6}{b-6}\) => \(\frac{a+5}{b+6}=\frac{a-5}{b-6}\)
Áp dụng t/c của dãy tỉ số bằng nhau ta có:
\(\frac{a+5}{b+6}=\frac{a-5}{b-6}=\frac{\left(a+5\right)+\left(a-5\right)}{\left(b+6\right)+\left(b-6\right)}=\frac{\left(a+5\right)-\left(a-5\right)}{\left(b+6\right)-\left(b-6\right)}\)
=> \(\frac{a}{b}=\frac{10}{12}=\frac{5}{6}\)
Vậy....
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