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