\(\frac{50}{51}\times\frac{51}{15}:\frac{34}{15}\)
\(=\frac{50}{51}\times\frac{51}{15}\times\frac{15}{34}\)
\(=\left(\frac{50}{51}\times\frac{51}{15}\right)\times\frac{15}{34}\)
\(=\frac{50}{15}\times\frac{15}{34}\)
\(=\frac{50}{34}=\frac{25}{17}\).