\(\dfrac{15}{34}+\dfrac{7}{21}+\dfrac{19}{34}-1\dfrac{15}{17}+\dfrac{2}{3}\\ =\left(\dfrac{15}{34}+\dfrac{19}{34}\right)+\dfrac{1}{3}+\dfrac{2}{3}-\dfrac{32}{17}\\ =\dfrac{34}{34}+\left(\dfrac{1}{3}+\dfrac{2}{3}\right)-\dfrac{32}{17}\\ =1+1-\dfrac{32}{17}\\ =2-\dfrac{32}{17}\\ =\dfrac{2\times17-32}{17}\\ =\dfrac{2}{17}\)
=(15/34+19/34)+(7/21+2/3)-32/17=34/34+(7/21+14/21)-32/17=1+21/21-32/17=1+1-32/17=2-32/17=2/17