\(\dfrac{15}{34}-\dfrac{7}{21}+\dfrac{19}{34}-\dfrac{15}{17}-\dfrac{2}{3}\)
\(=\left(\dfrac{15}{34}+\dfrac{19}{34}\right)-\left(\dfrac{7}{21}+\dfrac{2}{3}\right)-\dfrac{15}{17}\)
\(=1-\left(\dfrac{7}{21}+\dfrac{14}{21}\right)-\dfrac{15}{17}\)
\(=1-1-\dfrac{15}{17}\)
\(=-\dfrac{15}{17}\)