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