Ta có : \(\frac{a+5}{a-5}=\frac{b+6}{b-6}\Rightarrow\frac{b-6}{a-5}=\frac{b+6}{a+5}\)
Áp dụng t/c dãy tỉ số bằng nhau :
\(\frac{b-6}{a-5}=\frac{b+6}{a+5}=\frac{\left(b+6\right)-\left(b-6\right)}{\left(a+5\right)-\left(a-5\right)}=\frac{12}{10}=\frac{6}{5}\)
\(\Rightarrow5\left(b-6\right)=6\left(a-5\right)\Leftrightarrow5b-30=6a-30\Leftrightarrow5b=6a\Leftrightarrow\frac{a}{b}=\frac{5}{6}\)
\(\frac{a+5}{a-5}=\frac{b+6}{b-6}\)
\(\Rightarrow\left(a+5\right)\left(b-6\right)=\left(a-5\right)\left(b+6\right)\)
\(ab-6a+5b-30=ab+6a-5b-30\)
\(5b-6a=6a-5b\)
\(6a=5b\Rightarrow\frac{a}{5}=\frac{b}{6}\)
nhân chéo là dễ nhất
\(\frac{a+5}{a-5}=\frac{b+6}{b-6}=>\left(a+5\right)\left(b-6\right)=\left(a-5\right)\left(b+6\right)\)
\(=>ab-6a+5b-30=ab+6a-5b-30\) (phân phối)
=>-6a+5b=6a-5b
=>6a-(-6a)=5b-(-5b)
=>12a=10b
=>a/b=10/12=5/6 đpcm
