[tex]\dfrac{\overline{abc}+\overline{bca}+\overline{cab}}{\overline{xyz}+\overline{yzx}+\overline{zxy}}=\dfrac{100a+10b+c+100b+10c+a+100c+10a+b}{100x+10y+z+100y+10z+x+100z+10x+y}\\
=\dfrac{111a+111b+111c}{111x+111y+111z}=\dfrac{111(a+b+c)}{111(x+y+z)}=\boxed{\dfrac{a+b+c}{x+y+z}}[/tex]
