Do a.a = b.c nên \(\frac{a}{b}=\frac{c}{a}\)
Cho \(\frac{a}{b}=\frac{a}{c}=k\)
Suy ra: a=b.k , c=a.k
ta có:
\(\frac{a+b}{a-b}=\frac{b.k+b}{b.k-b}=\frac{b.\left(k+1\right)}{b.\left(k-1\right)}=\frac{k+1}{k-1}\)
\(\frac{c+a}{c-a}=\frac{c.k+c}{c.k-c}=\frac{c.\left(k+1\right)}{c.\left(k-1\right)}=\frac{k+1}{k-1}\)
từ đó ta CMĐ