Ta có: \(\frac{\overline{abc}}{a+\overline{bc}}=\frac{\overline{bca}}{b+\overline{ca}}\)
=>\(\frac{100a+\overline{bc}}{a+\overline{bc}}=\frac{100b+\overline{ca}}{b+\overline{ca}}\)
=>\(\frac{a+\overline{bc}+99a}{a+\overline{bc}}=\frac{b+\overline{ca}+99b}{b+\overline{ca}}\)
=>\(1+\frac{99a}{a+\overline{bc}}=1+\frac{99b}{b+\overline{ca}}\)
=>\(\frac{99a}{a+\overline{bc}}=\frac{99b}{b+\overline{ca}}\)
=>\(\frac{a}{a+10b+c}=\frac{b}{b+10c+a}\)
=>a(b+10c+a)=b(a+10b+c)
=>\(a\left(b+\overline{ca}\right)=b\left(a+\overline{bc}\right)\)
=>\(ab+a\cdot\overline{ca}=ab+b\cdot\overline{bc}\)
=>\(a\cdot\overline{ca}=b\cdot\overline{bc}\)
=>\(\frac{a}{\overline{bc}}=\frac{b}{\overline{ca}}\)
