6. \(\frac{3}{x-19}=\frac{19}{x-3}\)

ОДЗ: \(x\ne19\), \(x\ne3\).

\(3(x-3)=19(x-19)\);
\(3x-9=19x-361\);
\(352=16x\);
\(x=22\).

Ответ: \(x=22\).